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
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Aug 28 2018
STATUS
approved