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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. 21
 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, ... MATHEMATICA 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; Table[A[n - k, k], {n, 0, nmax}, {k, n, 0, -1}] // Flatten (* Jean-François Alcover, Oct 04 2019 *) 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: A198062 A347617 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 June 12 23:19 EDT 2024. Contains 373360 sequences. (Running on oeis4.)