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 A359990 #8 Feb 16 2025 08:34:04 %S A359990 0,1,1,3,11,3,7,105,105,7,15,919,3665,919,15,31,7713,123215,123215, %T A359990 7713,31,63,63351,4051679,16222021,4051679,63351,63,127,514321, %U A359990 131630449,2108725953,2108725953,131630449,514321,127,255,4148839,4248037953,272179739279,1089224690733,272179739279,4248037953,4148839,255 %N A359990 Array read by antidiagonals: T(m,n) is the number of edge cuts in the grid graph P_m X P_n. %C A359990 The complement of an edge cut is a disconnected spanning subgraph (spanning meaning that the graph has the same vertex set although some vertices may be of degree zero). %H A359990 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EdgeCut.html">Edge Cut</a> %H A359990 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GridGraph.html">Grid Graph</a> %F A359990 T(m,n) = 2^B(m,n) - A359993(m,n) where B(m,n) = 2*m*n - m - n = A141387(n+m-2, n-1) is the number of edges in the graph. %F A359990 T(m,n) = T(n,m). %e A359990 Table starts: %e A359990 ======================================================== %e A359990 m\n| 1 2 3 4 5 %e A359990 ---+---------------------------------------------------- %e A359990 1 | 0 1 3 7 15 ... %e A359990 2 | 1 11 105 919 7713 ... %e A359990 3 | 3 105 3665 123215 4051679 ... %e A359990 4 | 7 919 123215 16222021 2108725953 ... %e A359990 5 | 15 7713 4051679 2108725953 1089224690733 ... %e A359990 6 | 31 63351 131630449 272179739279 560238057496423 ... %e A359990 ... %Y A359990 Rows 1..3 are A000225(n-1), A359987, A359988. %Y A359990 Main diagonal is A359989. %Y A359990 Cf. A141387, A359993 (connected spanning subgraphs). %K A359990 nonn,tabl %O A359990 1,4 %A A359990 _Andrew Howroyd_, Jan 28 2023