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A318557
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Number A(n,k) of n-member subsets of [k*n] whose elements sum to a multiple of k; square array A(n,k), n>=0, k>=0, read by antidiagonals.
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21
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1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 2, 1, 0, 1, 1, 5, 10, 1, 0, 1, 1, 6, 30, 38, 1, 0, 1, 1, 9, 55, 165, 126, 1, 0, 1, 1, 10, 91, 460, 1001, 452, 1, 0, 1, 1, 13, 138, 969, 3876, 6198, 1716, 1, 0, 1, 1, 14, 190, 1782, 10630, 33594, 38760, 6470, 1, 0, 1, 1, 17, 253, 2925, 23751, 118755, 296010, 245157, 24310, 1, 0
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OFFSET
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0,13
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COMMENTS
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The sequence of row n satisfies a linear recurrence with constant coefficients of order A018804(n) for n>0.
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LINKS
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EXAMPLE
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A(3,2) = 10: {1,2,3}, {1,2,5}, {1,3,4}, {1,3,6}, {1,4,5}, {1,5,6}, {2,3,5}, {2,4,6}, {3,4,5}, {3,5,6}.
A(2,3) = 5: {1,2}, {1,5}, {2,4}, {3,6}, {4,5}.
Square array A(n,k) begins:
1, 1, 1, 1, 1, 1, 1, 1, ...
0, 1, 1, 1, 1, 1, 1, 1, ...
0, 1, 2, 5, 6, 9, 10, 13, ...
0, 1, 10, 30, 55, 91, 138, 190, ...
0, 1, 38, 165, 460, 969, 1782, 2925, ...
0, 1, 126, 1001, 3876, 10630, 23751, 46376, ...
0, 1, 452, 6198, 33594, 118755, 324516, 749398, ...
0, 1, 1716, 38760, 296010, 1344904, 4496388, 12271518, ...
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MATHEMATICA
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nmax = 11; (* Program not suitable to compute a large number of terms. *)
A[n_, k_] := A[n, k] = Count[Subsets[Range[k n], {n}], s_ /; Divisible[Total[s], k]]; A[0, _] = 1;
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CROSSREFS
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Columns k=0-10 give: A000007, A000012, A119358, A318591, A318592, A318593, A318594, A318595, A318596, A318597, A318598.
Rows n=0-10 give: A000012, A057427, A042963 (for k>0), A318624, A318625, A318626, A318627, A318628, A318629, A318630, A318631.
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KEYWORD
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AUTHOR
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STATUS
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approved
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