Polygonal Number - Table of Values

Table of Values

s Name Formula n=1 2 3 4 5 6 7 8 9 10 Sum of Reciprocals OEIS number
3 Triangular ½(1n² + 1n) 1 3 6 10 15 21 28 36 45 55 A000217
4 Square ½(2n² - 0n) 1 4 9 16 25 36 49 64 81 100 A000290
5 Pentagonal ½(3n² - 1n) 1 5 12 22 35 51 70 92 117 145 A000326
6 Hexagonal ½(4n² - 2n) 1 6 15 28 45 66 91 120 153 190 A000384
7 Heptagonal ½(5n² - 3n) 1 7 18 34 55 81 112 148 189 235 \begin{matrix} \frac{1}{15}{\pi}{\sqrt{25-10\sqrt{5}}}+\frac{2}{3}\ln(5) \\ +\frac{{1}+\sqrt{5}}{3}\ln\left(\frac{1}{2}\sqrt{10-2\sqrt{5}}\right) \\ +\frac{{1}-\sqrt{5}}{3}\ln\left(\frac{1}{2}\sqrt{10+2\sqrt{5}}\right) \end{matrix} A000566
8 Octagonal ½(6n² - 4n) 1 8 21 40 65 96 133 176 225 280 A000567
9 Nonagonal ½(7n² - 5n) 1 9 24 46 75 111 154 204 261 325 A001106
10 Decagonal ½(8n² - 6n) 1 10 27 52 85 126 175 232 297 370 A001107
11 Hendecagonal ½(9n² - 7n) 1 11 30 58 95 141 196 260 333 415 A051682
12 Dodecagonal ½(10n² - 8n) 1 12 33 64 105 156 217 288 369 460 A051624
13 Tridecagonal ½(11n² - 9n) 1 13 36 70 115 171 238 316 405 505 A051865
14 Tetradecagonal ½(12n² - 10n) 1 14 39 76 125 186 259 344 441 550 A051866
15 Pentadecagonal ½(13n² - 11n) 1 15 42 82 135 201 280 372 477 595 A051867
16 Hexadecagonal ½(14n² - 12n) 1 16 45 88 145 216 301 400 513 640 A051868
17 Heptadecagonal ½(15n² - 13n) 1 17 48 94 155 231 322 428 549 685 A051869
18 Octadecagonal ½(16n² - 14n) 1 18 51 100 165 246 343 456 585 730 A051870
19 Nonadecagonal ½(17n² - 15n) 1 19 54 106 175 261 364 484 621 775 A051871
20 Icosagonal ½(18n² - 16n) 1 20 57 112 185 276 385 512 657 820 A051872
21 Icosihenagonal ½(19n² - 17n) 1 21 60 118 195 291 406 540 693 865 A051873
22 Icosidigonal ½(20n² - 18n) 1 22 63 124 205 306 427 568 729 910 A051874
23 Icositrigonal ½(21n² - 19n) 1 23 66 130 215 321 448 596 765 955 A051875
24 Icositetragonal ½(22n² - 20n) 1 24 69 136 225 336 469 624 801 1000 A051876

The On-Line Encyclopedia of Integer Sequences eschews terms using Greek prefixes (e.g., "octagonal") in favor of terms using numerals (i.e., "8-gonal").

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