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 A350818 #10 Feb 16 2025 08:34:02 %S A350818 1,1,1,1,1,1,1,2,2,1,1,1,4,1,1,1,3,4,4,3,1,1,1,12,1,12,1,1,1,4,8,9,9, %T A350818 8,4,1,1,1,32,1,79,1,32,1,1,1,5,16,16,27,27,16,16,5,1,1,1,80,1,408,1, %U A350818 408,1,80,1,1,1,6,32,25,81,64,64,81,25,32,6,1 %N A350818 Array read by antidiagonals: T(m,n) is the number of maximum independent sets in the m X n king graph. %C A350818 The maximum size of an independent set is the independence number which in the case of an m X n king graph is given by ceiling(m/2)*ceiling(n/2). %H A350818 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KingGraph.html">King Graph</a> %H A350818 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MaximumIndependentVertexSet.html">Maximum Independent Vertex Set</a> %F A350818 T(m,n) = T(n,m). %F A350818 T(2*m+1, 2*n+1) = 1. %F A350818 T(2*m, 2*n+1) = (1+m)^(1+n). %F A350818 T(2*m, 2*n) = A350819(m, n). %e A350818 Table begins: %e A350818 ============================================= %e A350818 m\n | 0 1 2 3 4 5 6 7 8 %e A350818 ----+---------------------------------------- %e A350818 0 | 1 1 1 1 1 1 1 1 1 ... %e A350818 1 | 1 1 2 1 3 1 4 1 5 ... %e A350818 2 | 1 2 4 4 12 8 32 16 80 ... %e A350818 3 | 1 1 4 1 9 1 16 1 25 ... %e A350818 4 | 1 3 12 9 79 27 408 81 1847 ... %e A350818 5 | 1 1 8 1 27 1 64 1 125 ... %e A350818 6 | 1 4 32 16 408 64 3600 256 26040 ... %e A350818 7 | 1 1 16 1 81 1 256 1 625 ... %e A350818 8 | 1 5 80 25 1847 125 26040 625 281571 ... %e A350818 ... %Y A350818 Cf. A018807, A245013, A332347, A350815, A350819. %K A350818 nonn,tabl %O A350818 0,8 %A A350818 _Andrew Howroyd_, Jan 17 2022