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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
OFFSET
0,3
LINKS
Christian Bean, Bjarki Gudmundsson, Henning Ulfarsson, Automatic discovery of structural rules of permutation classes, arXiv:1705.04109 [math.CO], 2017.
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved