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A273526 Number of 123-avoiding indecomposable permutations. 8
1, 1, 3, 11, 38, 127, 423, 1423, 4854, 16787, 58776, 208001, 742888, 2674427, 9694831, 35357655, 129644774, 477638683, 1767263172, 6564120401, 24466267000, 91482563619, 343059613628, 1289904147301, 4861946401428, 18367353072127, 69533550915978, 263747951750333, 1002242216651340, 3814986502092275 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Indranil Ghosh, Table of n, a(n) for n = 1..1000

A. L. L. Gao, S. Kitaev, P. B. Zhang. On pattern avoiding indecomposable permutations, arXiv:1605.05490 [math.CO], 2016.

Murray Tannock, Equivalence classes of mesh patterns with a dominating pattern, MSc Thesis, Reykjavik Univ., May 2016.

FORMULA

a(n) = C(n) - n + 1, where C(n) is the Catalan number.

MATHEMATICA

a[n_] := CatalanNumber[n] - (n - 1)

Table[a[n], {n, 1, 30}] (* Alice L.L. Gao, May 24 2016 *)

PROG

(PARI)

a(n) = binomial(2*n, n)/(n+1) - n + 1; \\ Indranil Ghosh, Mar 04 2017

(Python)

import math

f=math.factorial

def C(n, r): return f(n)/f(r)/f(n-r)

def Catalan(n): return C(2*n, n)/(n+1)

def A273526(n): return Catalan(n)-n+1 # Indranil Ghosh, Mar 04 2017

CROSSREFS

Cf. A000108, A003319.

Sequence in context: A026361 A006189 A092201 * A026943 A047096 A149060

Adjacent sequences:  A273523 A273524 A273525 * A273527 A273528 A273529

KEYWORD

nonn

AUTHOR

Alice L.L. Gao and Philip B. Zhang, May 24 2016

STATUS

approved

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Last modified October 20 14:06 EDT 2018. Contains 316379 sequences. (Running on oeis4.)