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%I #9 Dec 12 2024 21:54:56
%S 0,1,1,3,6,3,7,22,22,7,15,84,150,84,15,31,346,1276,1276,346,31,63,
%T 1476,11538,23214,11538,1476,63,127,6322,102772,418912,418912,102772,
%U 6322,127,255,26844,890130,7290534,14673870,7290534,890130,26844,255,511,112666,7525876,123174016,496484776,496484776,123174016,7525876,112666,511
%N Array read by antidiagonals: T(m,n) is the number of minimal edge cuts in the rook graph K_m X K_n.
%H Andrew Howroyd, <a href="/A378935/b378935.txt">Table of n, a(n) for n = 1..1275</a> (first 50 antidiagonals)
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MinimalEdgeCut.html">Minimal Edge Cut</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RookGraph.html">Rook Graph</a>.
%F T(m,n) = A360873(m,n) + (2^(m-1) - 1)*(2^(n-1) - 1) - 2^(m*n-1).
%F T(m,n) = T(n,m).
%e Array begins:
%e ======================================================
%e m\n | 1 2 3 4 5 6 ...
%e ----+-------------------------------------------------
%e 1 | 0 1 3 7 15 31 ...
%e 2 | 1 6 22 84 346 1476 ...
%e 3 | 3 22 150 1276 11538 102772 ...
%e 4 | 7 84 1276 23214 418912 7290534 ...
%e 5 | 15 346 11538 418912 14673870 496484776 ...
%e 6 | 31 1476 102772 7290534 496484776 32893769886 ...
%e ...
%o (PARI) \\ Needs G from A360873.
%o T(M,N=M) = {G(M,N) + matrix(M,N,m,n, (2^(m-1) - 1)*(2^(n-1) - 1) - 2^(m*n-1))}
%o { my(A=T(7)); for(n=1, #A~, print(A[n,])) }
%Y Main diagonal is A378936.
%Y Rows 1..2 are A000225(n-1), A378937.
%Y Cf. A143088, A360873, A378932.
%K nonn,tabl,new
%O 1,4
%A _Andrew Howroyd_, Dec 12 2024