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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
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
Main diagonal gives A318477.
Sequence in context: A198062 A347617 A226690 * A245683 A273712 A129634
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.)