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A342372
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Triangle T(n,k) of number of ways of arranging q nonattacking semi-queens on an n X n toroidal board, where 0 <= k <= n.
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1
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1, 1, 1, 1, 4, 0, 1, 9, 9, 3, 1, 16, 48, 32, 0, 1, 25, 150, 250, 75, 15, 1, 36, 360, 1200, 1224, 288, 0, 1, 49, 735, 4165, 8869, 6321, 931, 133, 1, 64, 1344, 11648, 43136, 64512, 33024, 4096, 0, 1, 81, 2268, 27972, 160866, 423306, 469800
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OFFSET
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1,5
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COMMENTS
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T(0,0):=1 for combinatorial reasons.
A semi-queen can only move horizontal, vertical and parallel to the main diagonal of the board. Moves parallel to the secondary diagonal are not allowed.
Instead of a board on a torus, you can imagine that the semi-queens can leave a flat board on one side and re-enter the board on the other side.
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LINKS
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FORMULA
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T(n,0) = 1.
T(n,1) = n^2.
T(n,2) = n^2*(n-1)*(n-2)/2.
T(n,3) = n^2*(n-1)*(n-2)*(n^2-6n+10)/6.
T(2n,2n) = 0.
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EXAMPLE
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1;
1, 1;
1, 4, 0;
1, 9, 9, 3;
1, 16, 48, 32, 0;
1, 25, 150, 250, 75, 15;
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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