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„Sokszögszámok” változatai közötti eltérés

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2. sor:
 
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|}
 
8 ⟶ 13 sor:
 
:{|
|-
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|}
 
14 ⟶ 23 sor:
 
:{|
|-
|- align="center" valign="bottom"
| align="center" valign="bottom" |
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|}
 
Megegyezés szerint bármilyen oldalú sokszögszám esetén 1 a legelső szám. A második szám szükségképpen a sokszög csúcsainak száma. A sokszög megnagyobbítása úgy történik, hogy két szomszédos oldalát kiterjesztjük egy pöttyel, majd elvégezzük a pontok közötti szükséges kiegészítést. A következő ábrákon a hozzáadott réteget piros színnel jelöljük.
 
'''[[Háromszögszámok]]:'''
[[Fájl:Polygonal Number 3.gif|500px|none]]
 
'''[[Négyzetszámok]]:'''
[[Fájl:Polygonal Number 4.gif|500px|none]]
 
A000290 The squares: a(n) = n^2. [http://www.research.att.com/~njas/sequences/?q=0%2C+1%2C+4%2C+9%2C+16%2C+25%2C+36%2C+49%2C+64%2C+81%2C+100%2C+121%2C+144%2C+169%2C+196%2C+225%2C+256%2C+289%2C+324%2C+361%2C+400%2C+441%2C+484%2C+529%2C+576%2C+625%2C+676%2C+729%2C+784%2C+841%2C+900%2C+961%2C+1024%2C+1089%2C+1156%2C+1225%2C+1296%2C+1369%2C+1444%2C+1521%2C+1600%2C+1681%2C+1764%2C&sort=0&fmt=0&language=english&go=Search]
 
'''[[Ötszögszámok]]:''':
[[Fájl:Polygonal Number 5.gif|500px|none]]
A000326 Pentagonal numbers: n(3n-1)/2. [http://www.research.att.com/~njas/sequences/A000326]
 
'''[[Hatszögszámok]]:'''
[[Fájl:Polygonal Number 6.gif|500px|none]]
 
47 ⟶ 68 sor:
vagy
 
:<math>P(s,n) = (s-2)\frac{n(n-1)}{2}+n.</math>.
 
{| borderclass="3" cellpadding="3wikitable"
|- align=right
|-----
|! alignrowspan="center"2 | '''Név'''
|! alignrowspan="center"2 | '''Képlet'''
|! aligncolspan="center"13 | '''''n'' =1'''
|- align="center" | '''2'''right
! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8 !! 9 !! 10 !! 11 !! 12 !! 13
| align="center" | '''3'''
|- align="center" | '''4'''right
! Háromszögszám
| align="center" | '''5'''
! ½''n''(1''n'' + 1)
| align="center" | '''6'''
| 1 || 3 || 6 || 10 || 15 || 21 || 28 || 36 || 45 || 55 || 66 || 78 || 91
| align="center" | '''7'''
|- align="center" | '''8'''right
! Négyzetszám
| align="center" | '''9'''
! ½''n''(2''n'' – 0)
| align="center" | '''10'''
| 1 || 4 || 9 || 16 || 25 || 36 || 49 || 64 || 81 || 100 || 121 || 144 || 169
| align="center" | '''11'''
|- align="center" | '''12'''right
! Ötszögszám
| align="center" | '''13'''
! ½''n''(3''n'' – 1)
|-----
| 1 || 5 || 12 || 22 || 35 || 51 || 70 || 92 || 117 || 145 || 176 || 210 || 247
| align="center" | '''Háromszögszám'''
|- align="center" | ½''n''(1''n'' + 1)right
! Hatszögszám
| align="right" | 1 || align="right" | 3
! ½''n''(4''n'' – 2)
| align="right" | 6
| 1 || 6 || 15 || 28 || 45 || 66 || 91 || 120 || 153 || 190 || 231 || 276 || 325
| align="right" | 10 || align="right" | 15
|- align="right" | 21
! Hétszögszám
| align="right" | 28 || align="right" | 36
! ½''n''(5''n'' – 3)
| align="right" | 45
| 1 || 7 || 18 || 34 || 55 || 81 || 112 || 148 || 189 || 235 || 286 || 342 || 403
| align="right" | 55 || align="right" | 66
|- align="right" | 78 || align="right" | 91
! Nyolcszögszám
|-----
! ½''n''(6''n'' – 4)
| align="center" | '''Négyzetszám'''
| 1 || 8 || 21 || 40 || 65 || 96 || 133 || 176 || 225 || 280 || 341 || 408 || 481
| align="center" | ½''n''(2''n'' – 0)
|- align="right" | 1 || align="right" | 4
! Kilencszögszám
| align="right" | 9
! ½''n''(7''n'' – 5)
| align="right" | 16 || align="right" | 25
| 1 || 9 || 24 || 46 || 75 || 111 || 154 || 204 || 261 || 325 || 396 || 474 || 559
| align="right" | 36
|- align="right" | 49 || align="right" | 64
! Tízszögszám
| align="right" | 81
! ½''n''(8''n'' – 6)
| align="right" | 100 || align="right" | 121
| 1 || 10 || 27 || 52 || 85 || 126 || 175 || 232 || 297 || 370 || 451 || 540 || 637
| align="right" | 144 || align="right" | 169
|- align=right
|-----
! 11-szögszám
| align="center" | '''Ötszögszám'''
| align="center" |! ½''n''(39''n'' – 17)
| 1 || 11 || 30 || 58 || 95 || 141 || 196 || 260 || 333 || 415 || 506 || 606 || 715
| align="right" | 1 || align="right" | 5
|- align="right" | 12
! 12-szögszám
| align="right" | 22 || align="right" | 35
! ½''n''(10''n'' – 8)
| align="right" | 51
| 1 || 12 || 33 || 64 || 105 || 156 || 217 || 288 || 369 || 460 || 561 || 672 || 793
| align="right" | 70 || align="right" | 92
|- align="right" | 117
! 13-szögszám
| align="right" | 145 || align="right" | 176
! ½''n''(11''n'' – 9)
| align="right" | 210 || align="right" | 247
| 1 || 13 || 36 || 70 || 115 || 171 || 238 || 316 || 405 || 505 || 616 || 738 || 871
|-----
|- align="center" | '''Hatszögszám'''right
! 14-szögszám
| align="center" | ½''n''(4''n'' – 2)
! ½''n''(12''n'' – 10)
| align="right" | 1 || align="right" | 6
| 1 || 14 || 39 || 76 || 125 || 186 || 259 || 344 || 441 || 550 || 671 || 804 || 949
| align="right" | 15
|- align="right" | 28 || align="right" | 45
! 15-szögszám
| align="right" | 66
! ½''n''(13''n'' – 11)
| align="right" | 91 || align="right" | 120
| 1 || 15 || 42 || 82 || 135 || 201 || 280 || 372 || 477 || 595 || 726 || 870 || 1027
| align="right" | 153
|- align="right" | 190 || align="right" | 231
! 16-szögszám
| align="right" | 276 || align="right" | 325
! ½''n''(14''n'' – 12)
|-----
| 1 || 16 || 45 || 88 || 145 || 216 || 301 || 400 || 513 || 640 || 781 || 936 || 1105
| align="center" | '''Hétszögszám'''
|- align=right
| align="center" | ½''n''(5''n'' – 3)
! 17-szögszám
| align="right" | 1 || align="right" | 7
! ½''n''(15''n'' – 13)
| align="right" | 18
| 1 || 17 || 48 || 94 || 155 || 231 || 322 || 428 || 549 || 685 || 836 || 1002 || 1183
| align="right" | 34 || align="right" | 55
|- align="right" | 81
! 18-szögszám
| align="right" | 112 || align="right" | 148
! ½''n''(16''n'' – 14)
| align="right" | 189
| 1 || 18 || 51 || 100 || 165 || 246 || 343 || 456 || 585 || 730 || 891 || 1068 || 1261
| align="right" | 235 || align="right" | 286
|- align="right" | 342 || align="right" | 403
! 19-szögszám
|-----
! ½''n''(17''n'' – 15)
| align="center" | '''Nyolcszögszám'''
| 1 || 19 || 54 || 106 || 175 || 261 || 364 || 484 || 621 || 775 || 946 || 1134 || 1339
| align="center" | ½''n''(6''n'' – 4)
|- align="right" | 1 || align="right" | 8
! 20-szögszám
| align="right" | 21
! ½''n''(18''n'' – 16)
| align="right" | 40 || align="right" | 65
| 1 || 20 || 57 || 112 || 185 || 276 || 385 || 512 || 657 || 820 || 1001 || 1200 || 1417
| align="right" | 96
|- align="right" | 133 || align="right" | 176
! 21-szögszám
| align="right" | 225
! ½''n''(19''n'' – 17)
| align="right" | 280 || align="right" | 341
| 1 || 21 || 60 || 118 || 195 || 291 || 406 || 540 || 693 || 865 || 1056 || 1266 || 1495
| align="right" | 408 || align="right" | 481
|- align=right
|-----
! 22-szögszám
| align="center" | '''Kilencszögszám'''
| align="center" |! ½''n''(720''n'' – 518)
| 1 || 22 || 63 || 124 || 205 || 306 || 427 || 568 || 729 || 910 || 1111 || 1332 || 1573
| align="right" | 1 || align="right" | 9
|- align="right" | 24
! 23-szögszám
| align="right" | 46 || align="right" | 75
! ½''n''(21''n'' – 19)
| align="right" | 111
| 1 || 23 || 66 || 130 || 215 || 321 || 448 || 596 || 765 || 955 || 1166 || 1398 || 1651
| align="right" | 154 || align="right" | 204
|- align="right" | 261
! 24-szögszám
| align="right" | 325 || align="right" | 396
! ½''n''(22''n'' – 20)
| align="right" | 474 || align="right" | 559
| 1 || 24 || 69 || 136 || 225 || 336 || 469 || 624 || 801 || 1000 || 1221 || 1464 || 1729
|-----
|- align=right
| align="center" | '''Tízszögszám'''
! 25-szögszám
| align="center" | ½''n''(8''n'' – 6)
! ½''n''(23''n'' – 21)
| align="right" | 1 || align="right" | 10
| 1 || 25 || 72 || 142 || 235 || 351 || 490 || 652 || 837 || 1045 || 1276 || 1530 || 1807
| align="right" | 27
|- align="right" | 52 || align="right" | 85
! 26-szögszám
| align="right" | 126
! ½''n''(24''n'' – 22)
| align="right" | 175 || align="right" | 232
| 1 || 26 || 75 || 148 || 245 || 366 || 511 || 680 || 873 || 1090 || 1331 || 1596 || 1885
| align="right" | 297
|- align="right" | 370 || align="right" | 451
! 27-szögszám
| align="right" | 540 || align="right" | 637
! ½''n''(25''n'' – 23)
|-----
| 1 || 27 || 78 || 154 || 255 || 381 || 532 || 708 || 909 || 1135 || 1386 || 1662 || 1963
| align="center" | '''11-szögszám'''
|- align=right
| align="center" | ½''n''(9''n'' – 7)
! 28-szögszám
| align="right" | 1 || align="right" | 11
! ½''n''(26''n'' – 24)
| align="right" | 30
| 1 || 28 || 81 || 160 || 265 || 396 || 553 || 736 || 945 || 1180 || 1441 || 1728 || 2041
| align="right" | 58 || align="right" | 95
|- align="right" | 141
! 29-szögszám
| align="right" | 196 || align="right" | 260
! ½''n''(27''n'' – 25)
| align="right" | 333
| 1 || 29 || 84 || 166 || 275 || 411 || 574 || 764 || 981 || 1225 || 1496 || 1794 || 2119
| align="right" | 415 || align="right" | 506
|- align="right" | 606 || align="right" | 715
! 30-szögszám
|-----
! ½''n''(28''n'' – 26)
| align="center" | '''12-szögszám'''
| 1 || 30 || 87 || 172 || 285 || 426 || 595 || 792 || 1017 || 1270 || 1551 || 1860 || 2197
| align="center" | ½''n''(10''n'' – 8)
| align="right" | 1 || align="right" | 12
| align="right" | 33
| align="right" | 64 || align="right" | 105
| align="right" | 156
| align="right" | 217 || align="right" | 288
| align="right" | 369
| align="right" | 460 || align="right" | 561
| align="right" | 672 || align="right" | 793
|-----
| align="center" | '''13-szögszám'''
| align="center" | ½''n''(11''n'' – 9)
| align="right" | 1 || align="right" | 13
| align="right" | 36
| align="right" | 70 || align="right" | 115
| align="right" | 171
| align="right" | 238 || align="right" | 316
| align="right" | 405
| align="right" | 505 || align="right" | 616
| align="right" | 738 || align="right" | 871
|-----
| align="center" | '''14-szögszám'''
| align="center" | ½''n''(12''n'' – 10)
| align="right" | 1 || align="right" | 14
| align="right" | 39
| align="right" | 76 || align="right" | 125
| align="right" | 186
| align="right" | 259 || align="right" | 344
| align="right" | 441
| align="right" | 550 || align="right" | 671
| align="right" | 804 || align="right" | 949
|-----
| align="center" | '''15-szögszám'''
| align="center" | ½''n''(13''n'' – 11)
| align="right" | 1 || align="right" | 15
| align="right" | 42
| align="right" | 82 || align="right" | 135
| align="right" | 201
| align="right" | 280 || align="right" | 372
| align="right" | 477
| align="right" | 595 || align="right" | 726
| align="right" | 870 || align="right" | 1027
|-----
| align="center" | '''16-szögszám'''
| align="center" | ½''n''(14''n'' – 12)
| align="right" | 1 || align="right" | 16
| align="right" | 45
| align="right" | 88 || align="right" | 145
| align="right" | 216
| align="right" | 301 || align="right" | 400
| align="right" | 513
| align="right" | 640 || align="right" | 781
| align="right" | 936 || align="right" | 1105
|-----
| align="center" | '''17-szögszám'''
| align="center" | ½''n''(15''n'' – 13)
| align="right" | 1 || align="right" | 17
| align="right" | 48
| align="right" | 94 || align="right" | 155
| align="right" | 231
| align="right" | 322 || align="right" | 428
| align="right" | 549
| align="right" | 685 || align="right" | 836
| align="right" | 1002 || align="right" | 1183
|-----
| align="center" | '''18-szögszám'''
| align="center" | ½''n''(16''n'' – 14)
| align="right" | 1 || align="right" | 18
| align="right" | 51
| align="right" | 100 || align="right" | 165
| align="right" | 246
| align="right" | 343 || align="right" | 456
| align="right" | 585
| align="right" | 730 || align="right" | 891
| align="right" | 1068 || align="right" | 1261
|-----
| align="center" | '''19-szögszám'''
| align="center" | ½''n''(17''n'' – 15)
| align="right" | 1 || align="right" | 19
| align="right" | 54
| align="right" | 106 || align="right" | 175
| align="right" | 261
| align="right" | 364 || align="right" | 484
| align="right" | 621
| align="right" | 775 || align="right" | 946
| align="right" | 1134 || align="right" | 1339
|-----
| align="center" | '''20-szögszám'''
| align="center" | ½''n''(18''n'' – 16)
| align="right" | 1 || align="right" | 20
| align="right" | 57
| align="right" | 112 || align="right" | 185
| align="right" | 276
| align="right" | 385 || align="right" | 512
| align="right" | 657
| align="right" | 820 || align="right" | 1001
| align="right" | 1200 || align="right" | 1417
|-----
| align="center" | '''21-szögszám'''
| align="center" | ½''n''(19''n'' – 17)
| align="right" | 1 || align="right" | 21
| align="right" | 60
| align="right" | 118 || align="right" | 195
| align="right" | 291
| align="right" | 406 || align="right" | 540
| align="right" | 693
| align="right" | 865 || align="right" | 1056
| align="right" | 1266 || align="right" | 1495
|-----
| align="center" | '''22-szögszám'''
| align="center" | ½''n''(20''n'' – 18)
| align="right" | 1 || align="right" | 22
| align="right" | 63
| align="right" | 124 || align="right" | 205
| align="right" | 306
| align="right" | 427 || align="right" | 568
| align="right" | 729
| align="right" | 910 || align="right" | 1111
| align="right" | 1332 || align="right" | 1573
|-----
| align="center" | '''23-szögszám'''
| align="center" | ½''n''(21''n'' – 19)
| align="right" | 1 || align="right" | 23
| align="right" | 66
| align="right" | 130 || align="right" | 215
| align="right" | 321
| align="right" | 448 || align="right" | 596
| align="right" | 765
| align="right" | 955 || align="right" | 1166
| align="right" | 1398 || align="right" | 1651
|-----
| align="center" | '''24-szögszám'''
| align="center" | ½''n''(22''n'' – 20)
| align="right" | 1 || align="right" | 24
| align="right" | 69
| align="right" | 136 || align="right" | 225
| align="right" | 336
| align="right" | 469 || align="right" | 624
| align="right" | 801
| align="right" | 1000 || align="right" | 1221
| align="right" | 1464 || align="right" | 1729
|-----
| align="center" | '''25-szögszám'''
| align="center" | ½''n''(23''n'' – 21)
| align="right" | 1 || align="right" | 25
| align="right" | 72
| align="right" | 142 || align="right" | 235
| align="right" | 351
| align="right" | 490 || align="right" | 652
| align="right" | 837
| align="right" | 1045 || align="right" | 1276
| align="right" | 1530 || align="right" | 1807
|-----
| align="center" | '''26-szögszám'''
| align="center" | ½''n''(24''n'' – 22)
| align="right" | 1 || align="right" | 26
| align="right" | 75
| align="right" | 148 || align="right" | 245
| align="right" | 366
| align="right" | 511 || align="right" | 680
| align="right" | 873
| align="right" | 1090 || align="right" | 1331
| align="right" | 1596 || align="right" | 1885
|-----
| align="center" | '''27-szögszám'''
| align="center" | ½''n''(25''n'' – 23)
| align="right" | 1 || align="right" | 27
| align="right" | 78
| align="right" | 154 || align="right" | 255
| align="right" | 381
| align="right" | 532 || align="right" | 708
| align="right" | 909
| align="right" | 1135 || align="right" | 1386
| align="right" | 1662 || align="right" | 1963
|-----
| align="center" | '''28-szögszám'''
| align="center" | ½''n''(26''n'' – 24)
| align="right" | 1 || align="right" | 28
| align="right" | 81
| align="right" | 160 || align="right" | 265
| align="right" | 396
| align="right" | 553 || align="right" | 736
| align="right" | 945
| align="right" | 1180 || align="right" | 1441
| align="right" | 1728 || align="right" | 2041
|-----
| align="center" | '''29-szögszám'''
| align="center" | ½''n''(27''n'' – 25)
| align="right" | 1 || align="right" | 29
| align="right" | 84
| align="right" | 166 || align="right" | 275
| align="right" | 411
| align="right" | 574 || align="right" | 764
| align="right" | 981
| align="right" | 1225 || align="right" | 1496
| align="right" | 1794 || align="right" | 2119
|-----
| align="center" | '''30-szögszám'''
| align="center" | ½''n''(28''n'' – 26)
| align="right" | 1 || align="right" | 30
| align="right" | 87
| align="right" | 172 || align="right" | 285
| align="right" | 426
| align="right" | 595 || align="right" | 792
| align="right" | 1017
| align="right" | 1270 || align="right" | 1551
| align="right" | 1860 || align="right" | 2197
|}
 
A lap eredeti címe: „https://hu.wikipedia.org/wiki/Sokszögszámok”