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A071076 Number of permutations that avoid the generalized pattern 123-4. 4
1, 1, 2, 6, 23, 108, 598, 3815, 27532, 221708, 1970251, 19150132, 202064380, 2300071071, 28092017668, 366425723926, 5083645400819, 74745472084176, 1160974832572274, 18995175706664735, 326531476287842760, 5883736110875887560, 110893188848753125475 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..450

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 [math.CO], 2011.

S. Kitaev, Partially Ordered Generalized Patterns

S. Kitaev, Partially Ordered Generalized Patterns, Discrete Math. 298 (2005), no. 1-3, 212-229.

FORMULA

E.g.f.: exp(int(A(y), y=0..x)), where A(y) = (sqrt(3)/2)*exp(y/2)/cos((sqrt(3)/2)*y + Pi/6).

MAPLE

b:= proc(u, o, t) option remember; `if`(u+o=0, 1, add(

      `if`(t=1 and o>j, 0, b(u+j-1, o-j, t+1)), j=1..o)+

       add(b(u-j, o+j-1, 0), j=1..u))

    end:

a:= n-> b(n, 0$2):

seq(a(n), n=0..25);  # Alois P. Heinz, Nov 14 2015

MATHEMATICA

b[u_, o_, t_] := b[u, o, t] = If[u + o == 0, 1, Sum[If[t == 1 && o > j, 0, b[u + j - 1, o - j, t + 1]], {j, 1, o}] + Sum[b[u - j, o + j - 1, 0], {j, 1, u}]]; a[n_] := b[n, 0, 0]; Table[a[n], {n, 0, 25}] (* Jean-Fran├žois Alcover, Feb 01 2016, after Alois P. Heinz *)

CROSSREFS

Cf. A071088, A071075, A071077.

Sequence in context: A007555 A101053 A155857 * A297196 A112501 A093345

Adjacent sequences:  A071073 A071074 A071075 * A071077 A071078 A071079

KEYWORD

nonn

AUTHOR

Sergey Kitaev (kitaev(AT)math.chalmers.se), May 26 2002

EXTENSIONS

More terms from Vladeta Jovovic, May 28 2002

Link added by Andrew Baxter, May 17 2011

Typos in formula corrected by Vaclav Kotesovec, Aug 23 2014

STATUS

approved

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Last modified February 20 00:28 EST 2019. Contains 320329 sequences. (Running on oeis4.)