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 A367304 #20 Jan 06 2024 12:00:02 %S A367304 1,4,1,27,8,1,130,88,16,1,385,444,246,30,1,1044,1544,1376,492,57,1, %T A367304 2005,3584,4621,2814,1079,88,1,4060,8356,11691,9042,6014,1800,163,1, %U A367304 6831,14996,25026,23604,20049,10016,3196,230,1,11272,26572,47386,50448,50597,34432,17632,4770,386,1 %N A367304 Table read by antidiagonals: Place k equally spaced points on each side of a regular n-gon and join every pair of these n*k points by a chord; T(n,k) (n >= 3, k >= 0) gives the number of regions in the resulting planar graph. %C A367304 See A367278 and A006533 for other images of the n-gons. %H A367304 Scott R. Shannon, <a href="/A367304/a367304.png">Image for T(5,5)</a>. %H A367304 Scott R. Shannon, <a href="/A367304/a367304_1.png">Image for T(7,4)</a>. %H A367304 Scott R. Shannon, <a href="/A367304/a367304_2.png">Image for T(8,4)</a>. %H A367304 Scott R. Shannon, <a href="/A367304/a367304_3.png">Image for T(12,3)</a>. %F A367304 a(n,k) = A367305(n,k) - A367302(n,k) + 1 (Euler). %e A367304 The table begins: %e A367304 1, 4, 27, 130, 385, 1044, 2005, 4060, 6831, 11272, 16819, 26436, 35737, 52147, ... %e A367304 1, 8, 88, 444, 1544, 3584, 8356, 14996, 26572, 42144, 69988, 93264, 148364, ... %e A367304 1, 16, 246, 1376, 4621, 11691, 25026, 47386, 82096, 133076, 204716, 301861, ... %e A367304 1, 30, 492, 2814, 9042, 23604, 50448, 95244, 163890, 268848, 415146, 610476, ... %e A367304 1, 57, 1079, 6014, 20049, 50597, 107171, 201916, 348559, 563375, 864977, ... %e A367304 1, 88, 1800, 10016, 34432, 86360, 185856, 347976, 604248, 974184, 1502416, ... %e A367304 1, 163, 3196, 17632, 58195, 146071, 308296, 578926, 997219, 1609453, 2467720, ... %e A367304 1, 230, 4770, 26470, 89160, 222730, 474120, 887230, 1532880, 2470640, 3798120, ... %e A367304 1, 386, 7525, 41053, 134729, 336678, 708753, 1327987, 2284151, 3682306, ... %e A367304 1, 456, 9276, 56100, 187872, 468660, 1002300, 1873824, 3235104, 5214684, ... %e A367304 1, 794, 15250, 82447, 269309, 670892, 1409630, 2637051, 4530891, ... %e A367304 1, 966, 20286, 109956, 363552, 902174, 1904504, 3555020, 6119918, ... %e A367304 1, 1471, 27811, 149266, 485761, 1207201, 2532751, 4732516, 8124511, ... %e A367304 . %e A367304 . %e A367304 . %Y A367304 Cf. A367302 (vertices), A367303 (internal vertices), A367305 (edges), A366486 (first row), A367278 (second row), A006533 (second column). %K A367304 nonn,tabl %O A367304 3,2 %A A367304 _Scott R. Shannon_, Nov 13 2023