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 A384120 #9 May 20 2025 19:16:18 %S A384120 1,1,1,1,2,1,1,4,4,1,1,8,9,8,1,1,16,18,18,16,1,1,32,35,34,35,32,1,1, %T A384120 64,68,62,62,68,64,1,1,128,133,114,105,114,133,128,1,1,256,262,214, %U A384120 180,180,214,262,256,1,1,512,519,410,319,286,319,410,519,512,1 %N A384120 Array read by antidiagonals: T(n,m) is the number of cliques in the n X m rook graph K_n X K_m. %C A384120 Also the number of independent vertex sets in the n X m rook complement graph. %H A384120 Andrew Howroyd, <a href="/A384120/b384120.txt">Table of n, a(n) for n = 0..1325</a> (first 51 antidiagonals) %H A384120 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Clique.html">Clique</a>. %H A384120 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RookGraph.html">Rook Graph</a>. %F A384120 T(n,m) = 1 + n*(2^m - 1) + m*(2^n - 1) - n*m. %F A384120 T(n,m) = T(m,n). %e A384120 Array begins: %e A384120 ================================================= %e A384120 n\m | 0 1 2 3 4 5 6 7 8 ... %e A384120 ----+------------------------------------------- %e A384120 0 | 1 1 1 1 1 1 1 1 1 ... %e A384120 1 | 1 2 4 8 16 32 64 128 256 ... %e A384120 2 | 1 4 9 18 35 68 133 262 519 ... %e A384120 3 | 1 8 18 34 62 114 214 410 798 ... %e A384120 4 | 1 16 35 62 105 180 319 586 1109 ... %e A384120 5 | 1 32 68 114 180 286 472 818 1484 ... %e A384120 6 | 1 64 133 214 319 472 721 1162 1987 ... %e A384120 7 | 1 128 262 410 586 818 1162 1730 2746 ... %e A384120 8 | 1 256 519 798 1109 1484 1987 2746 4017 ... %e A384120 ... %o A384120 (PARI) T(n,m) = 1 + n*(2^m - 1) + m*(2^n - 1) - n*m %Y A384120 Main diagonal is A288958. %Y A384120 Columns 0..3 are A000012, A000079, A083706, A250770(n-1). %Y A384120 Cf. A384121. %K A384120 nonn,tabl,easy %O A384120 0,5 %A A384120 _Andrew Howroyd_, May 20 2025