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

Author

Lara Pudwell, Feb 26 2006

Keywords

• nonn
• easy

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

• Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A000108, A001263.

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

Extensions

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