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A188920 a(n) is the limiting term of the n-th column of the triangle in A188919. 2
1, 1, 2, 4, 7, 13, 22, 38, 63, 105, 169, 274, 434, 686, 1069, 1660, 2548, 3897, 5906, 8911, 13352, 19917, 29532, 43605, 64056, 93715, 136499, 198059, 286233, 412199, 591455, 845851, 1205687, 1713286, 2427177, 3428611, 4829563, 6784550, 9505840, 13284849 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..39.

A. M. Baxter, Algorithms for Permutation Statistics, Ph. D. Dissertation, Rutgers University, May 2011

Andrew M. Baxter and Lara K. Pudwell, Enumeration schemes for dashed patterns, arXiv preprint arXiv:1108.2642, 2011

MATHEMATICA

b[u_, o_] := b[u, o] = Expand[If[u + o == 0, 1, Sum[b[u - j, o + j - 1]*x^(o + j - 1), {j, 1, u}] + Sum[If[u == 0, b[u + j - 1, o - j]*x^(o - j), 0], {j, 1, o}]]];

T[n_] := Function[p, Table[Coefficient[p, x, i], {i, 0, Exponent[p, x]}]][ b[0, n]];

Take[T[40], 40] (* Jean-Fran├žois Alcover, Sep 15 2018, after Alois P. Heinz in A188919 *)

CROSSREFS

Sequence in context: A192758 A085489 A101268 * A281362 A319111 A128768

Adjacent sequences:  A188917 A188918 A188919 * A188921 A188922 A188923

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Apr 13 2011

EXTENSIONS

More terms from Andrew Baxter, May 17 2011

a(30)-a(39) from Alois P. Heinz, Nov 14 2015

STATUS

approved

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Last modified March 22 01:06 EDT 2019. Contains 321406 sequences. (Running on oeis4.)