A295873 Number of permutations of length n which avoid the patterns 1342, 2413, 3124 and 3142.

1, 1, 2, 6, 20, 68, 231, 781, 2629, 8821, 29530, 98706, 329592, 1099792, 3668127, 12230505, 40771337, 135895689, 452914658, 1509385902, 5029980252, 16761785436, 55855539047, 186125915029, 620217261197, 2066704787645, 6886704234970, 22947920663130, 76467083518464

Offset

0,3

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Christian Bean, Bjarki Gudmundsson, Henning Ulfarsson, Automatic discovery of structural rules of permutation classes, arXiv:1705.04109 [math.CO], 2017.

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

Formula

G.f.: (1-6*x+11*x^2-6*x^3+x^4)/(1-7*x+16*x^2-14*x^3+5*x^4-x^5).

From Colin Barker, Dec 27 2017: (Start)

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

a(n) = 7*a(n-1) - 16*a(n-2) + 14*a(n-3) - 5*a(n-4) + a(n-5) for n>4.

(End)

Prog

(PARI) Vec((1 - 3*x + x^2)^2 / ((1 - x)*(1 - 6*x + 10*x^2 - 4*x^3 + x^4)) + O(x^40)) \\ Colin Barker, Dec 27 2017

Crossrefs

Sequence in context: A291005 A027065 A231057 * A006012 A127152 A279557

Adjacent sequences: A295870 A295871 A295872 * A295874 A295875 A295876

Keyword

nonn,easy

Author

Bjarki Ágúst Guðmundsson, Dec 26 2017

Status

approved