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

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

Keyword

nonn,easy

Author

Lara Pudwell, Feb 26 2006

Extensions

a(0)=1 prepended by Alois P. Heinz, Nov 28 2021

Status

approved