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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.)