A116746 Number of permutations of length n which avoid the patterns 1243, 4123, 4213.

1, 2, 6, 21, 75, 262, 890, 2949, 9575, 30590, 96486, 301269, 933171, 2872102, 8794946, 26822901, 81539855, 247232702, 748061070, 2259653349, 6816525435, 20540701510, 61842968906, 186063857829, 559486534391, 1681592864702, 5052356855286, 15175393904181, 45570473759235

Offset

1,2

Links

Table of n, a(n) for n=1..29.

David Callan and Toufik Mansour, Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns, arXiv:1705.00933 [math.CO] (2017), Table 2 No 160.

Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.

Index entries for linear recurrences with constant coefficients, signature (8,-22,22,-1,-6).

Formula

G.f.: -x*(4*x^4 + 5*x^3 - 12*x^2 + 6*x - 1)/((x - 1)*(3*x - 1)*(2*x - 1)*(x^2 + 2*x - 1)).

For n > 0, a(n) = 2^n + 2*3^(n-1) - ((1 + sqrt(2))^(n+2) + (1 - sqrt(2))^(n+2))/4 + 1/2. - Vaclav Kotesovec, Jan 19 2026

Mathematica

LinearRecurrence[{8, -22, 22, -1, -6}, {1, 2, 6, 21, 75}, 40] (* Harvey P. Dale, Jul 25 2018 *)

Crossrefs

Sequence in context: A294814 A116816 A116742 * A116806 A116736 A116820

Adjacent sequences: A116743 A116744 A116745 * A116747 A116748 A116749

Keyword

nonn,easy

Author

Lara Pudwell, Feb 26 2006

Extensions

a(27)-a(29) from Stefano Spezia, Jan 19 2026

Status

approved