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A191928
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Array read by antidiagonals: T(m,n) = floor(m/2)*floor((m-1)/2)*floor(n/2)*floor((n-1)/2).
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2
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 6, 8, 8, 6, 0, 0, 0, 0, 0, 0, 9, 12, 16, 12, 9, 0, 0, 0, 0, 0, 0, 12, 18, 24, 24, 18, 12, 0, 0, 0, 0, 0, 0, 16, 24, 36, 36, 36, 24, 16, 0, 0, 0, 0, 0, 0, 20, 32, 48, 54, 54, 48, 32, 20, 0, 0, 0, 0, 0, 0, 25, 40, 64, 72, 81, 72, 64, 40, 25, 0, 0, 0
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OFFSET
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0,32
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COMMENTS
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T(m,n) is conjectured to be the crossing number of the complete bipartite graph K_{m,n}.
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LINKS
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FORMULA
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EXAMPLE
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Array begins:
0, 0, 0, 0, 0, 0, 0, 0, 0, ...
0, 0, 0, 0, 0, 0, 0, 0, 0, ...
0, 0, 0, 0, 0, 0, 0, 0, 0, ...
0, 0, 0, 1, 2, 4, 6, 9, 12, ...
0, 0, 0, 2, 4, 8, 12, 18, 24, ...
0, 0, 0, 4, 8, 16, 24, 36, 48, ...
0, 0, 0, 6, 12, 24, 36, 54, 72, ...
0, 0, 0, 9, 18, 36, 54, 81, 108, ...
0, 0, 0, 12, 24, 48, 72, 108, 144, ...
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MAPLE
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K:=(m, n)->floor(m/2)*floor((m-1)/2)*floor(n/2)*floor((n-1)/2);
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PROG
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(PARI) T(n, k) = ((n-1)^2\4)*((k-1)^2\4);
tabl(nn) = for (n=0, nn, for (k=0, n, print1(T(n, k), ", ")); print()); \\ Michel Marcus, Sep 30 2017
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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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