A116844 - OEIS

A116844

Number of permutations of length n which avoid the patterns 231, 12345.

1, 1, 2, 5, 14, 41, 116, 302, 715, 1549, 3106, 5831, 10352, 17525, 28484, 44696, 68021, 100777, 145810, 206569, 287186, 392561, 528452, 701570, 919679, 1191701, 1527826, 1939627, 2440180, 3044189, 3768116, 4630316, 5651177, 6853265, 8261474, 9903181, 11808406

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OFFSET

0,3

COMMENTS

a(n) is the number of Dyck n-paths (A000108) with <= 4 peaks. So a(n) is the sum of columns 1,2,3,4 in the Narayana triangle A001263. - David Callan, Jul 03 2006

LINKS

Table of n, a(n) for n=0..36.

Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

FORMULA

G.f.: -(4*x^6 - 8*x^5 + 21*x^4 - 23*x^3 + 16*x^2 - 6*x + 1)/(x-1)^7.

a(n) = (n^6 - 9n^5 + 43n^4 - 99n^3 + 172n^2 - 108n + 144)/144. - Franklin T. Adams-Watters, Sep 16 2006

Equals A001263 * [1, 1, 1, 1, 0, 0, 0, ...] - Gary W. Adamson, Nov 19 2007

CROSSREFS

Cf. A000108, A001263.

Sequence in context: A225691 A116846 A080558 * A116851 A038989 A116850

Adjacent sequences: A116841 A116842 A116843 * A116845 A116846 A116847