A116811 Number of permutations of length n which avoid the patterns 1234, 1432, 3214.

1, 2, 6, 21, 70, 204, 560, 1617, 4796, 14249, 41939, 122658, 358991, 1053628, 3095381, 9089525, 26674879, 78271099, 229705211, 674214603, 1978919196, 5808153968, 17046573229, 50030848109, 146839772058, 430974323821, 1264905691383, 3712476662089

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..1000

D. Callan, T. Mansour, Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns, arXiv:1705.00933 (2017), Table 2 No 13.

Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.

Index entries for linear recurrences with constant coefficients, signature (2,1,2,5,14,7,-25,-25,-17,-10,-16,-1).

Formula

G.f.: -x*(x^11 +16*x^10 +10*x^9 +17*x^8 +25*x^7 +25*x^6 -7*x^5 -13*x^4 -5*x^3 -x^2 -1) / (x^12 +16*x^11 +10*x^10 +17*x^9 +25*x^8 +25*x^7 -7*x^6 -14*x^5 -5*x^4 -2*x^3 -x^2 -2*x +1). [Rewritten in a more conventional form by Colin Barker, May 26 2015]

Prog

(PARI) Vec(-x*(x^11 +16*x^10 +10*x^9 +17*x^8 +25*x^7 +25*x^6 -7*x^5 -13*x^4 -5*x^3 -x^2 -1) / (x^12 +16*x^11 +10*x^10 +17*x^9 +25*x^8 +25*x^7 -7*x^6 -14*x^5 -5*x^4 -2*x^3 -x^2 -2*x +1) + O(x^100)) \\ Colin Barker, May 26 2015

Crossrefs

Sequence in context: A116815 A116804 A116832 * A294718 A116794 A294719

Adjacent sequences: A116808 A116809 A116810 * A116812 A116813 A116814

Keyword

nonn,easy

Author

Lara Pudwell, Feb 26 2006

Status

approved