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 A384121 #6 May 20 2025 19:16:08 %S A384121 1,1,1,1,1,1,1,1,1,1,1,1,9,1,1,1,1,39,39,1,1,1,1,183,421,183,1,1,1,1, %T A384121 833,3825,3825,833,1,1,1,1,3629,32047,64727,32047,3629,1,1,1,1,15291, %U A384121 260355,1046425,1046425,260355,15291,1,1,1,1,63051,2092909,16771879,33548731,16771879,2092909,63051,1,1 %N A384121 Array read by antidiagonals: T(n,m) is the number of dominating sets in the n X m rook complement graph. %C A384121 Non-dominating sets are just those that are contained in the union of a single row and column minus the intersecting vertex. %H A384121 Andrew Howroyd, <a href="/A384121/b384121.txt">Table of n, a(n) for n = 0..1325</a> (first 51 antidiagonals) %H A384121 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DominatingSet.html">Dominating Set</a>. %H A384121 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RookComplementGraph.html">Rook Complement Graph</a>. %F A384121 T(n,m) = 2^(n*m) - n*(2^m-2) - m*(2^n-2) + n*m - n*m*(2^(m-1)-1)*(2^(n-1)-1) + n*(n-1)*m*(m-1)/2 - 1 for n > 1, m > 1. %F A384121 T(n,m) = T(m,n). %e A384121 Array begins: %e A384121 =============================================================== %e A384121 n\m | 0 1 2 3 4 5 6 ... %e A384121 ----+---------------------------------------------------------- %e A384121 0 | 1 1 1 1 1 1 1 ... %e A384121 1 | 1 1 1 1 1 1 1 ... %e A384121 2 | 1 1 9 39 183 833 3629 ... %e A384121 3 | 1 1 39 421 3825 32047 260355 ... %e A384121 4 | 1 1 183 3825 64727 1046425 16771879 ... %e A384121 5 | 1 1 833 32047 1046425 33548731 1073727713 ... %e A384121 6 | 1 1 3629 260355 16771879 1073727713 68719441881 ... %e A384121 7 | 1 1 15291 2092909 268422785 34359704907 4398046428559 ... %e A384121 ... %o A384121 (PARI) T(n,m) = if(n<=1 || m<=1, 1, 2^(n*m) - n*(2^m-2) - m*(2^n-2) + n*m - n*m*(2^(m-1)-1)*(2^(n-1)-1) + n*(n-1)*m*(m-1)/2 - 1) %Y A384121 Main diagonal is A292073. %Y A384121 Columns 0 and 1 are A000012. %Y A384121 Column 2 is A287063, n > 1. %Y A384121 Cf. A384120 (independent sets), A384122, A384123. %K A384121 nonn,tabl %O A384121 0,13 %A A384121 _Andrew Howroyd_, May 20 2025