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A264909
Number A(n,k) of k-ascent sequences of length n with no consecutive repeated letters; square array A(n,k), n>=0, k>=0, read by antidiagonals.
12
1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 2, 2, 0, 1, 1, 3, 6, 5, 0, 1, 1, 4, 12, 21, 16, 0, 1, 1, 5, 20, 54, 87, 61, 0, 1, 1, 6, 30, 110, 276, 413, 271, 0, 1, 1, 7, 42, 195, 670, 1574, 2213, 1372, 0, 1, 1, 8, 56, 315, 1380, 4470, 9916, 13205, 7795, 0
OFFSET
0,13
LINKS
S. Kitaev, J. Remmel, p-Ascent Sequences, arXiv:1503.00914 [math.CO], 2015.
EXAMPLE
Square array A(n,k) begins:
1, 1, 1, 1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, 6, 7, ...
0, 2, 6, 12, 20, 30, 42, 56, ...
0, 5, 21, 54, 110, 195, 315, 476, ...
0, 16, 87, 276, 670, 1380, 2541, 4312, ...
0, 61, 413, 1574, 4470, 10555, 21931, 41468, ...
0, 271, 2213, 9916, 32440, 86815, 201761, 422128, ...
MAPLE
b:= proc(n, k, i, t) option remember; `if`(n<1, 1, add(
`if`(j=i, 0, b(n-1, k, j, t+`if`(j>i, 1, 0))), j=0..t+k))
end:
A:= (n, k)-> b(n-1, k, 0$2):
seq(seq(A(n, d-n), n=0..d), d=0..12);
MATHEMATICA
b[n_, k_, i_, t_] := b[n, k, i, t] = If[n<1, 1, Sum[If[j == i, 0, b[n-1, k, j, t + If[j>i, 1, 0]]], {j, 0, t+k}]]; A[n_, k_] := b[n-1, k, 0, 0]; Table[Table[A[n, d-n], {n, 0, d}], {d, 0, 12}] // Flatten (* Jean-François Alcover, Feb 17 2016, after Alois P. Heinz *)
CROSSREFS
Rows k=0+1,2-4 give: A000012, A001477, A002378, A160378(n+1).
Main diagonal gives A264916.
Sequence in context: A112555 A108561 A174626 * A104579 A079531 A182882
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Nov 28 2015
STATUS
approved