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A343097
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Array read by antidiagonals: T(n,k) is the number of k-colorings of an n X n grid, up to rotations and reflections.
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16
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1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 3, 6, 1, 0, 1, 4, 21, 102, 1, 0, 1, 5, 55, 2862, 8548, 1, 0, 1, 6, 120, 34960, 5398083, 4211744, 1, 0, 1, 7, 231, 252375, 537157696, 105918450471, 8590557312, 1, 0, 1, 8, 406, 1284066, 19076074375, 140738033618944, 18761832172500795, 70368882591744, 1, 0
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OFFSET
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0,8
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LINKS
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FORMULA
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T(n,k) = (k^(n^2) + 2*k^((n^2 + 3*(n mod 2))/4) + k^((n^2 + (n mod 2))/2) + 2*k^(n*(n+1)/2) + 2*k^(n*(n + n mod 2)/2) )/8.
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EXAMPLE
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Array begins:
====================================================================
n\k | 0 1 2 3 4 5
----+---------------------------------------------------------------
0 | 1 1 1 1 1 1 ...
1 | 0 1 2 3 4 5 ...
2 | 0 1 6 21 55 120 ...
3 | 0 1 102 2862 34960 252375 ...
4 | 0 1 8548 5398083 537157696 19076074375 ...
5 | 0 1 4211744 105918450471 140738033618944 37252918396015625 ...
...
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PROG
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(PARI) T(n, k) = {(k^(n^2) + 2*k^((n^2 + 3*(n%2))/4) + k^((n^2 + (n%2))/2) + 2*k^(n*(n+1)/2) + 2*k^(n*(n+n%2)/2) )/8}
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CROSSREFS
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Columns 0..10 are A000007, A000012, A054247, A054739, A054751, A054752, A286392, A286393, A286394, A286396, A286397.
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KEYWORD
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AUTHOR
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STATUS
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approved
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