A116820 Number of permutations of length n which avoid the patterns 2341, 3241, 4213.

1, 2, 6, 21, 75, 264, 914, 3127, 10621, 35932, 121324, 409301, 1380417, 4655382, 15700590, 52954137, 178609067, 602449564, 2032105066, 6854506171, 23121097405, 77990499392, 263072412420, 887378656761, 2993247393297, 10096624106970, 34057260581510

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 [math.CO] (2017), Table 2 No 168 and 169.

Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.

Index entries for linear recurrences with constant coefficients, signature (8,-23,29,-14,1)

Formula

G.f.: x*(1 - 6*x + 13*x^2 - 10*x^3 + x^4) / ((1 - x)*(1 - 7*x + 16*x^2 - 13*x^3 + x^4)).

a(n) = 8*a(n-1) - 23*a(n-2) + 29*a(n-3) - 14*a(n-4) + a(n-5) for n>5. - Colin Barker, Oct 18 2017

Prog

(PARI) Vec(x*(1 - 6*x + 13*x^2 - 10*x^3 + x^4) / ((1 - x)*(1 - 7*x + 16*x^2 - 13*x^3 + x^4)) + O(x^30)) \\ Colin Barker, Oct 18 2017

Crossrefs

Sequence in context: A116746 A116806 A116736 * A369626 A294815 A116751

Adjacent sequences: A116817 A116818 A116819 * A116821 A116822 A116823

Keyword

nonn,easy

Author

Lara Pudwell, Feb 26 2006

Status

approved