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 A341850 #10 Feb 16 2025 08:34:01 %S A341850 1,1,1,1,1,1,1,1,1,1,1,3,2,3,1,1,3,4,4,3,1,1,15,16,72,16,15,1,1,15,56, %T A341850 132,132,56,15,1,1,105,376,7020,2016,7020,376,105,1,1,105,1912,17280, %U A341850 44928,44928,17280,1912,105,1,1,945,17984,1920240,1551744,22615200,1551744,1920240,17984,945,1 %N A341850 Array read by antidiagonals: T(n,m) is the number of maximum matchings in the rook graph K_n X K_m. %C A341850 In the case that both m and n are odd a single vertex is not covered, otherwise the maximum matchings are perfect matchings. %H A341850 Andrew Howroyd, <a href="/A341850/b341850.txt">Table of n, a(n) for n = 0..527</a> %H A341850 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MaximumIndependentEdgeSet.html">Maximum Independent Edge Set</a> %H A341850 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RookGraph.html">Rook Graph</a> %F A341850 T(n,m) = T(m,n). %e A341850 Array begins: %e A341850 ====================================================== %e A341850 n\m | 0 1 2 3 4 5 6 %e A341850 ----+------------------------------------------------- %e A341850 0 | 1 1 1 1 1 1 1 ... %e A341850 1 | 1 1 1 3 3 15 15 ... %e A341850 2 | 1 1 2 4 16 56 376 ... %e A341850 3 | 1 3 4 72 132 7020 17280 ... %e A341850 4 | 1 3 16 132 2016 44928 1551744 ... %e A341850 5 | 1 15 56 7020 44928 22615200 243319680 ... %e A341850 6 | 1 15 376 17280 1551744 243319680 61903180800 ... %e A341850 ... %Y A341850 Rows n=1..4 are A133221(n+1), A081919, A341851, A341852. %Y A341850 Main diagonal is A289197. %Y A341850 Cf. A270227 (matchings), A286070, A341847 (maximal matchings). %K A341850 nonn,tabl %O A341850 0,12 %A A341850 _Andrew Howroyd_, Feb 21 2021