This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A357254 #22 Sep 21 2022 12:00:37 %S A357254 3,9,4,27,12,5,57,36,15,6,99,76,45,18,7,135,132,95,54,21,8,219,180, %T A357254 165,114,63,24,9,297,292,255,198,133,72,27,10,351,348,365,306,231,152, %U A357254 81,30,11,489,516,495,438,357,264,171,90,33,12,603,604,645,594,511,408,297,190,99,36,13 %N A357254 Table read by antidiagonals: T(n,k) (n >= 3, k >= 0) is the number of edges in an n-gon when k internal n-gons are drawn between the n*k points that divide each side into k+1 equal parts. %C A357254 Conjecture: the only n-gons that contain non-simple intersections are the 3-gon (triangle), 4-gon (square), and 6-gon (hexagon). %H A357254 Scott R. Shannon, <a href="/A357254/a357254.txt">Extended table for n = 3..50, k = 0..75</a>. %F A357254 T(n,k) = A357216(n,k) + A357235(n,k) - 1 by Euler's formula. %F A357254 T(n,0) = n. %F A357254 T(n,1) = 3n. %F A357254 Conjectured formula for all columns for n >= 7: T(n,k) = 2n*k^2 + n. %F A357254 T(3,k) = A357008(k). %F A357254 T(4,k) = A357061(k). %F A357254 T(6,k) = A357198(k). %F A357254 Conjectured formula for all rows except for n = 3, 4, 6: T(n,k) = 2n*k^2 + n. %e A357254 The table begins: %e A357254 3, 9, 27, 57, 99, 135, 219, 297, 351, 489, 603, 645, 867, 1017, ... %e A357254 4, 12, 36, 76, 132, 180, 292, 348, 516, 604, 804, 892, 1156, 1284, ... %e A357254 5, 15, 45, 95, 165, 255, 365, 495, 645, 815, 1005, 1215, 1445, 1695, ... %e A357254 6, 18, 54, 114, 198, 306, 438, 594, 774, 942, 1206, 1422, 1734, 2034, ... %e A357254 7, 21, 63, 133, 231, 357, 511, 693, 903, 1141, 1407, 1701, 2023, 2373, ... %e A357254 8, 24, 72, 152, 264, 408, 584, 792, 1032, 1304, 1608, 1944, 2312, 2712, ... %e A357254 9, 27, 81, 171, 297, 459, 657, 891, 1161, 1467, 1809, 2187, 2601, 3051, ... %e A357254 10, 30, 90, 190, 330, 510, 730, 990, 1290, 1630, 2010, 2430, 2890, 3390, ... %e A357254 11, 33, 99, 209, 363, 561, 803, 1089, 1419, 1793, 2211, 2673, 3179, 3729, ... %e A357254 12, 36, 108, 228, 396, 612, 876, 1188, 1548, 1956, 2412, 2916, 3468, 4068, ... %e A357254 13, 39, 117, 247, 429, 663, 949, 1287, 1677, 2119, 2613, 3159, 3757, 4407, ... %e A357254 14, 42, 126, 266, 462, 714, 1022, 1386, 1806, 2282, 2814, 3402, 4046, 4746, ... %e A357254 15, 45, 135, 285, 495, 765, 1095, 1485, 1935, 2445, 3015, 3645, 4335, 5085, ... %e A357254 ... %e A357254 See the attached text file for further examples. %e A357254 See A356984, A357058, A357196 for images of the n-gons. %Y A357254 Cf. A357216 (regions), A357235 (vertices), A357008 (triangle), A357061 (square), A357198 (hexagon), A356984, A357058, A357196, A135565, A344899. %K A357254 nonn,tabl %O A357254 3,1 %A A357254 _Scott R. Shannon_, Sep 20 2022