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 A318557 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. 20
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,13 COMMENTS The sequence of row n satisfies a linear recurrence with constant coefficients of order A018804(n) for n>0. LINKS Alois P. Heinz, Antidiagonals n = 0..85, flattened EXAMPLE 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, ... CROSSREFS 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. Main diagonal gives A318477. Cf. A018804, A304482. Sequence in context: A263857 A198062 A226690 * A245683 A273712 A129634 Adjacent sequences:  A318554 A318555 A318556 * A318558 A318559 A318560 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Aug 28 2018 STATUS approved

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Last modified May 24 10:48 EDT 2019. Contains 323529 sequences. (Running on oeis4.)