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A378935 Array read by antidiagonals: T(m,n) is the number of minimal edge cuts in the rook graph K_m X K_n.

%I A378935 #10 Feb 16 2025 08:34:07
%S A378935 0,1,1,3,6,3,7,22,22,7,15,84,150,84,15,31,346,1276,1276,346,31,63,
%T A378935 1476,11538,23214,11538,1476,63,127,6322,102772,418912,418912,102772,
%U A378935 6322,127,255,26844,890130,7290534,14673870,7290534,890130,26844,255,511,112666,7525876,123174016,496484776,496484776,123174016,7525876,112666,511
%N A378935 Array read by antidiagonals: T(m,n) is the number of minimal edge cuts in the rook graph K_m X K_n.
%H A378935 Andrew Howroyd, <a href="/A378935/b378935.txt">Table of n, a(n) for n = 1..1275</a> (first 50 antidiagonals)
%H A378935 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MinimalEdgeCut.html">Minimal Edge Cut</a>.
%H A378935 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RookGraph.html">Rook Graph</a>.
%F A378935 T(m,n) = A360873(m,n) + (2^(m-1) - 1)*(2^(n-1) - 1) - 2^(m*n-1).
%F A378935 T(m,n) = T(n,m).
%e A378935 Array begins:
%e A378935 ======================================================
%e A378935 m\n |  1    2      3       4         5           6 ...
%e A378935 ----+-------------------------------------------------
%e A378935   1 |  0    1      3       7        15          31 ...
%e A378935   2 |  1    6     22      84       346        1476 ...
%e A378935   3 |  3   22    150    1276     11538      102772 ...
%e A378935   4 |  7   84   1276   23214    418912     7290534 ...
%e A378935   5 | 15  346  11538  418912  14673870   496484776 ...
%e A378935   6 | 31 1476 102772 7290534 496484776 32893769886 ...
%e A378935   ...
%o A378935 (PARI) \\ Needs G from A360873.
%o A378935 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 A378935 { my(A=T(7)); for(n=1, #A~, print(A[n,])) }
%Y A378935 Main diagonal is A378936.
%Y A378935 Rows 1..2 are A000225(n-1), A378937.
%Y A378935 Cf. A143088, A360873, A378932.
%K A378935 nonn,tabl
%O A378935 1,4
%A A378935 _Andrew Howroyd_, Dec 12 2024