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A295873 Number of permutations of length n which avoid the patterns 1342, 2413, 3124 and 3142. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 4 13:09 EDT 2020. Contains 336201 sequences. (Running on oeis4.)