cp's OEIS Frontend

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.

A367303 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 internal vertices in the resulting planar graph.

This page as a plain text file.
%I A367303 #18 Jan 06 2024 11:59:44
%S A367303 0,0,0,13,1,0,96,57,5,0,285,329,200,13,0,901,1317,1265,379,35,0,1605,
%T A367303 2861,4410,2437,987,49,0,3534,7417,11280,7843,5789,1577,126,0,5797,
%U A367303 12801,24455,21235,19642,9193,3042,161,0,9813,23329,46570,46141,49931,33161,17280,4371,330,0
%N A367303 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 internal vertices in the resulting planar graph.
%C A367303 See A366484 and A367277 for other images of the n-gons.
%H A367303 Scott R. Shannon, <a href="/A367303/a367303.png">Image for T(5,5)</a>.
%H A367303 Scott R. Shannon, <a href="/A367303/a367303_1.png">Image for T(8,3)</a>.
%H A367303 Scott R. Shannon, <a href="/A367303/a367303_2.png">Image for T(12,2)</a>.
%F A367303 a(n,k) = A367305(n,k) - A367304(n,k) + 1 - n*(k+1) (Euler).
%e A367303 The table begins:
%e A367303 0, 0, 13, 96, 285, 901, 1605, 3534, 5797, 9813, 14319, 23809, 30912, 47154, ...
%e A367303 0, 1, 57, 329, 1317, 2861, 7417, 12801, 23329, 36549, 64625, 80085, 138261, ...
%e A367303 0, 5, 200, 1265, 4410, 11280, 24455, 46570, 80960, 131510, 202555, 298630, ...
%e A367303 0, 13, 379, 2437, 7843, 21235, 46141, 87427, 150391, 249925, 388819, 569767, ...
%e A367303 0, 35, 987, 5789, 19642, 49931, 106120, 200508, 346619, 560602, 861252, ...
%e A367303 0, 49, 1577, 9193, 33161, 83313, 182649, 341369, 597097, 961681, 1490601, ...
%e A367303 0, 126, 3042, 17280, 57510, 145008, 306621, 576711, 994149, 1605267, 2462013, ...
%e A367303 0, 161, 4371, 25161, 87251, 218151, 469331, 877211, 1522141, 2452131, 3781431, ...
%e A367303 0, 330, 7293, 40524, 133738, 335126, 706310, 1324763, 2279695, 3676321, ...
%e A367303 0, 301, 7861, 53077, 182653, 456181, 990145, 1849453, 3207217, 5171377, ...
%e A367303 0, 715, 14924, 81705, 267930, 668733, 1406275, 2632604, 4524793, ...
%e A367303 0, 757, 19447, 107101, 360319, 893033, 1896567, 3536275, 6103763, ...
%e A367303 0, 1365, 27375, 148275, 483930, 1204305, 2528340, 4726650, 8116515, ...
%e A367303 .
%e A367303 .
%e A367303 .
%Y A367303 Cf. A367302 (vertices), A367304 (regions), A367305 (edges), A366484 (first row), A367277 (second row).
%K A367303 nonn,tabl
%O A367303 3,4
%A A367303 _Scott R. Shannon_, Nov 13 2023