A116712 Number of permutations of length n which avoid the patterns 231, 3214, 4312.

1, 2, 5, 12, 27, 59, 126, 265, 551, 1136, 2327, 4743, 9630, 19493, 39363, 79336, 159659, 320915, 644414, 1293009, 2592783, 5196512, 10410735, 20850127, 41746622, 83568269, 167257931, 334712280, 669742371, 1339998971

Offset

1,2

Links

Table of n, a(n) for n=1..30.

Michael Dairyko, Lara Pudwell, Samantha Tyner, Casey Wynn, Non-contiguous pattern avoidance in binary trees. Electron. J. Combin. 19 (2012), no. 3, Paper 22, 21 pp. MR2967227. - From N. J. A. Sloane, Feb 01 2013

Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.

Index entries for linear recurrences with constant coefficients, signature (3,-1,-2).

Formula

G.f.: A(x) = (x^3-x+1)*x/((2*x-1)*(x^2+x-1)).

a(n) = A257113(n+1) - A000045(n+2). - R. J. Mathar, Nov 07 2017

Mathematica

CoefficientList[Series[(x^3-x+1)/((2*x-1)*(x^2+x-1)), {x, 0, 50}], x] (* Stefano Spezia, Nov 29 2018 *)

Crossrefs

Sequence in context: A129983 A307265 A083378 * A000102 A304175 A086589

Adjacent sequences: A116709 A116710 A116711 * A116713 A116714 A116715

Keyword

nonn,easy

Author

Lara Pudwell, Feb 26 2006

Status

approved