A116812 Number of permutations of length n which avoid the patterns 2314, 3421, 4123.

1, 2, 6, 21, 72, 229, 683, 1954, 5452, 14974, 40671, 109509, 292743, 777810, 2055833, 5409187, 14175902, 37020669, 96378274, 250204801, 647907945, 1673920904, 4315683002, 11105412898, 28527156939, 73161209063, 187350573875

Offset

1,2

Links

Table of n, a(n) for n=1..27.

D. Callan, T. Mansour, Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns, arXiv:1705.00933 (2017), Table 2 No 45.

Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.

Index entries for linear recurrences with constant coefficients, signature (10,-43,106,-167,174,-118,48,-9).

Formula

G.f.: A(x) = {x(x^9-2x^8-10x^7+35x^6-64x^5+75x^4-59x^3+29x^2-8x+1)}/{(x-1)^2(3x^3-5x^2+4x-1)^2}

Mathematica

LinearRecurrence[{10, -43, 106, -167, 174, -118, 48, -9}, {1, 2, 6, 21, 72, 229, 683, 1954, 5452, 14974}, 40] (* Harvey P. Dale, Sep 17 2023 *)

Crossrefs

Sequence in context: A116775 A116786 A116748 * A116830 A116747 A116810

Adjacent sequences: A116809 A116810 A116811 * A116813 A116814 A116815

Keyword

nonn,easy

Author

Lara Pudwell, Feb 26 2006

Status

approved