OFFSET
0,13
LINKS
Alois P. Heinz, Antidiagonals n = 0..20, flattened
P. Duncan and Einar Steingrimsson, Pattern avoidance in ascent sequences, arXiv:1109.3641, 2011
EXAMPLE
A(4,2) = 10: 0123, 0011, 0012, 0101, 0102, 0110, 0112, 0120, 0121, 0122.
Square array A(n,k) begins:
1, 1, 1, 1, 1, 1, 1, 1, 1, ...
0, 1, 1, 1, 1, 1, 1, 1, 1, ...
0, 1, 2, 2, 2, 2, 2, 2, 2, ...
0, 1, 4, 5, 5, 5, 5, 5, 5, ...
0, 1, 10, 14, 15, 15, 15, 15, 15, ...
0, 1, 27, 47, 52, 53, 53, 53, 53, ...
0, 1, 83, 180, 210, 216, 217, 217, 217, ...
0, 1, 277, 773, 964, 1006, 1013, 1014, 1014, ...
0, 1, 1015, 3701, 4960, 5270, 5326, 5334, 5335, ...
MAPLE
b:= proc(n, i, t, p, k) option remember; `if`(n=0, 1,
add(`if`(coeff(p, x, j)=k, 0, b(n-1, j, t+
`if`(j>i, 1, 0), p+x^j, k)), j=1..t+1))
end:
A:= (n, k)-> b(n, 0$3, min(n, k)):
seq(seq(A(n, d-n), n=0..d), d=0..12);
MATHEMATICA
b[n_, i_, t_, p_, k_] := b[n, i, t, p, k] = If[n == 0, 1, Sum[ If[ Coefficient[p, x, j] == k, 0, b[n-1, j, t + If[j>i, 1, 0], p + x^j, k]], {j, 1, t+1}]];
A[n_, k_] := b[n, 0, 0, 0, Min[n, k]];
Table[Table[A[n, d-n], {n, 0, d}], {d, 0, 11}] // Flatten (* Jean-François Alcover, Aug 05 2018, translated from Maple *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Oct 25 2017
STATUS
approved