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 A384118 #6 May 20 2025 12:52:07
%S A384118 1,1,1,1,0,1,1,1,1,1,1,3,4,3,1,1,6,5,5,6,1,1,10,12,51,12,10,1,1,15,37,
%T A384118 97,97,37,15,1,1,21,98,218,368,218,98,21,1,1,28,219,519,2229,2229,519,
%U A384118 219,28,1,1,36,430,1417,6232,7310,6232,1417,430,36,1
%N A384118 Array read by antidiagonals: T(n,m) is the number of minimal total dominating sets in the n X m rook graph K_n X K_m.
%H A384118 Andrew Howroyd, <a href="/A384118/b384118.txt">Table of n, a(n) for n = 0..1325</a> (first 51 antidiagonals)
%H A384118 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MinimalTotalDominatingSet.html">Minimal Total Dominating Set</a>.
%H A384118 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RookGraph.html">Rook Graph</a>.
%F A384118 T(n,m) = T(m,n).
%e A384118 Array begins:
%e A384118 =====================================================
%e A384118 n\m | 0 1 2 3 4 5 6 7 ...
%e A384118 ----+------------------------------------------------
%e A384118 0 | 1 1 1 1 1 1 1 1 ...
%e A384118 1 | 1 0 1 3 6 10 15 21 ...
%e A384118 2 | 1 1 4 5 12 37 98 219 ...
%e A384118 3 | 1 3 5 51 97 218 519 1417 ...
%e A384118 4 | 1 6 12 97 368 2229 6232 16013 ...
%e A384118 5 | 1 10 37 218 2229 7310 44491 172387 ...
%e A384118 6 | 1 15 98 519 6232 44491 301572 1345693 ...
%e A384118 7 | 1 21 219 1417 16013 172387 1345693 10893008 ...
%e A384118 ...
%o A384118 (PARI)
%o A384118 B(n,m)={ my(M=matrix(n+1,m+1)); for(n=1, n, M[n+1,1]=1; for(m=1, m, M[n+1,m+1] = if(n>2, binomial(n,2)*M[n-1,m]) + sum(i=2, m, binomial(m-1,i-1)*(n*M[n, m-i+1] + if(i>=3&&i<=n, binomial(n,i-1)*i!*M[n-i+2,m-i+1] ) )))); M}
%o A384118 A(n,m)={ my(M=B(m,n) + B(n,m)~); M[1,1]=1; for(i=1, m, for(j=1, n, if((i+j)%3==0 && j<=2*i && i<=2*j, my(t=(i+j)/3); M[i+1,j+1] += binomial(i,j-t)*binomial(j,i-t)*(2*(j-t))!*(2*(i-t))!/2^t ))); M}
%o A384118 { my(T=A(8,8)); for(i=1, #T, print(T[i, ])) }
%Y A384118 Main diagonal is A347921.
%Y A384118 Cf. A290632, A384116, A384117.
%K A384118 nonn,tabl
%O A384118 0,12
%A A384118 _Andrew Howroyd_, May 19 2025