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 A384122 #9 May 22 2025 16:57:42 %S A384122 1,1,1,1,1,1,1,1,1,1,1,1,4,1,1,1,1,3,3,1,1,1,1,4,48,4,1,1,1,1,5,100, %T A384122 100,5,1,1,1,1,6,185,240,185,6,1,1,1,1,7,306,480,480,306,7,1,1,1,1,8, %U A384122 469,840,1000,840,469,8,1,1,1,1,9,680,1344,1800,1800,1344,680,9,1,1 %N A384122 Array read by antidiagonals: T(n,m) is the number of minimum dominating sets in the n X m rook complement graph. %C A384122 For n >= 3, m >= 3, the minimum size of a dominating set is 3. %H A384122 Andrew Howroyd, <a href="/A384122/b384122.txt">Table of n, a(n) for n = 0..1325</a> (first 51 antidiagonals) %H A384122 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MinimumDominatingSet.html">Minimum Dominating Set</a>. %H A384122 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RookComplementGraph.html">Rook Complement Graph</a>. %F A384122 T(n,m) = 4*binomial(n,2)*binomial(m,2) + 6*binomial(n,3)*binomial(m,3) for n >= 4, m >= 4. %F A384122 T(n,m) = T(m,n). %F A384122 T(n,0) = T(n,1) = 1. %e A384122 Array begins: %e A384122 =============================================== %e A384122 n\m | 0 1 2 3 4 5 6 7 8 ... %e A384122 ----+------------------------------------------ %e A384122 0 | 1 1 1 1 1 1 1 1 1 ... %e A384122 1 | 1 1 1 1 1 1 1 1 1 ... %e A384122 2 | 1 1 4 3 4 5 6 7 8 ... %e A384122 3 | 1 1 3 48 100 185 306 469 680 ... %e A384122 4 | 1 1 4 100 240 480 840 1344 2016 ... %e A384122 5 | 1 1 5 185 480 1000 1800 2940 4480 ... %e A384122 6 | 1 1 6 306 840 1800 3300 5460 8400 ... %e A384122 7 | 1 1 7 469 1344 2940 5460 9114 14112 ... %e A384122 8 | 1 1 8 680 2016 4480 8400 14112 21952 ... %e A384122 ... %o A384122 (PARI) T(n,m) = if(n<=2||m<=2, if(n<=1||m<=1, 1, if(n==2,m)+if(m==2,n)), 4*binomial(n,2)*binomial(m,2) + 6*binomial(n,3)*binomial(m,3) + if(n==3,m) + if(m==3,n)) %Y A384122 Main diagonal is A292074. %Y A384122 Column 3 is A090197(n-1), n >= 4. %Y A384122 Column 4 is A272871(n), n >= 4. %Y A384122 Cf. A384121, A384123. %K A384122 nonn,tabl %O A384122 0,13 %A A384122 _Andrew Howroyd_, May 20 2025