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.

A286513 Array read by antidiagonals: T(m,n) is the number of independent sets in the stacked prism graph C_m X P_n.

This page as a plain text file.
%I A286513 #32 Jul 18 2025 09:33:34
%S A286513 1,1,3,1,7,4,1,17,13,7,1,41,43,35,11,1,99,142,181,81,18,1,239,469,933,
%T A286513 621,199,29,1,577,1549,4811,4741,2309,477,47,1,1393,5116,24807,36211,
%U A286513 26660,8303,1155,76,1,3363,16897,127913,276561,307983,143697,30277,2785,123
%N A286513 Array read by antidiagonals: T(m,n) is the number of independent sets in the stacked prism graph C_m X P_n.
%C A286513 Equivalently, the number of vertex covers in the stacked prism graph C_m X P_n.
%H A286513 Liang Kai, <a href="/A286513/b286513.txt">Table of n, a(n) for n = 1..704</a> (terms up to a(435) from Andrew Howroyd)
%H A286513 Kai Liang, <a href="https://arxiv.org/abs/2507.04007">Independent Set Enumeration and Estimation of Related Constants of Grid Graphs</a>, arXiv:2507.04007 [math.CO], 2025. See p. 13.
%H A286513 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IndependentVertexSet.html">Independent Vertex Set</a>.
%H A286513 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/StackedPrismGraph.html">Stacked Prism Graph</a>.
%H A286513 Wikipedia, <a href="https://en.wikipedia.org/wiki/Independent_set_(graph_theory)">Independent set</a>.
%e A286513 Table starts:
%e A286513 =============================================================
%e A286513 m\n|   1    2     3      4        5         6           7
%e A286513 ---|---------------------------------------------------------
%e A286513 1  |   1    1     1      1        1         1           1 ...
%e A286513 2  |   3    7    17     41       99       239         577 ...
%e A286513 3  |   4   13    43    142      469      1549        5116 ...
%e A286513 4  |   7   35   181    933     4811     24807      127913 ...
%e A286513 5  |  11   81   621   4741    36211    276561     2112241 ...
%e A286513 6  |  18  199  2309  26660   307983   3557711    41097664 ...
%e A286513 7  |  29  477  8303 143697  2488431  43089985   746156517 ...
%e A286513 8  |  47 1155 30277 788453 20546803 535404487 13951571713 ...
%e A286513 ...
%Y A286513 Rows 3..8 are A003688(n+1), A051926, A181989, A181961, A182014, A182019.
%Y A286513 Columns 1..4 are A000032, A051927, A050400, A050401.
%Y A286513 Main diagonal is A212270.
%Y A286513 Cf. A089934 (P_m X P_n), A027683, A286514.
%K A286513 nonn,tabl
%O A286513 1,3
%A A286513 _Andrew Howroyd_, May 10 2017