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%I #12 Dec 11 2024 17:57:10
%S 0,1,1,2,6,2,3,15,15,3,4,28,53,28,4,5,45,146,146,45,5,6,66,356,627,
%T 356,66,6,7,91,809,2471,2471,809,91,7,8,120,1759,9292,16213,9292,1759,
%U 120,8,9,153,3716,33878,103196,103196,33878,3716,153,9,10,190,7702,120771,642364,1123743,642364,120771,7702,190,10
%N Array read by antidiagonals: T(m,n) is the number of minimal edge cuts in the grid graph P_m X P_n.
%C T(m,n) is the number of partitionings of an m X n checkerboard into two edgewise-connected sets.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MinimalEdgeCut.html">Minimal Edge Cut</a>.
%F T(m,n) = T(n,m).
%e Table starts:
%e ===================================================
%e m\n | 1 2 3 4 5 6 7 ...
%e ----+----------------------------------------------
%e 1 | 0 1 2 3 4 5 6 ...
%e 2 | 1 6 15 28 45 66 91 ...
%e 3 | 2 15 53 146 356 809 1759 ...
%e 4 | 3 28 146 627 2471 9292 33878 ...
%e 5 | 4 45 356 2471 16213 103196 642364 ...
%e 6 | 5 66 809 9292 103196 1123743 12028981 ...
%e 7 | 6 91 1759 33878 642364 12028981 221984391 ...
%e ...
%Y Main diagonal is A068416.
%Y Rows 1..4 are A001477(n-1), A000384, A378933, A378934.
%Y Rows 3..8 multiplied by 2 are A166761, A166766, A166769, A166771, A166773, A166774.
%Y Cf. A287151, A359990.
%K nonn,tabl,new
%O 1,4
%A _Andrew Howroyd_, Dec 11 2024