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A071088 Number of permutations that avoid the generalized pattern 12345-6. 4
1, 1, 2, 6, 24, 120, 719, 5022, 40064, 359400, 3580896, 39233867, 468818397, 6067548429, 84551873634, 1262188317534, 20095114167065, 339883289813330, 6086154606429378, 115025120586250896, 2288119443771888504, 47787869441095495395, 1045507132393256095282 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

Sergey Kitaev, Partially Ordered Generalized Patterns, preprint.

Sergey 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) = 1/(Sum_{i>=0} y^{5*i}/(5*i)! - Sum_{i>=0} y^{5*i+1}/(5*i+1)!).

Let b(n) = A177523(n) = number of permutations of [n] that avoid the consecutive pattern 12345. Then a(n) = Sum_{i = 0..n-1} binomial(n-1,i)*b(i)*a(n-1-i) with a(0) = b(0) = 1. [See the recurrence for A_n and B_n in the proof of Theorem 13 in Kitaev's papers.] - Petros Hadjicostas, Nov 01 2019

MAPLE

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

      `if`(t=3 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

CROSSREFS

Cf. A071075, A071076, A071077, A177523.

Sequence in context: A052398 A047890 A297204 * A177533 A122417 A321008

Adjacent sequences:  A071085 A071086 A071087 * A071089 A071090 A071091

KEYWORD

nonn

AUTHOR

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

EXTENSIONS

More terms from Vladeta Jovovic, May 28 2002

STATUS

approved

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Last modified September 19 02:54 EDT 2020. Contains 337175 sequences. (Running on oeis4.)