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A116757
Number of permutations of length n which avoid the patterns 1324, 2314, 4312.
1
1, 2, 6, 21, 73, 238, 724, 2075, 5667, 14892, 37942, 94273, 229453, 548954, 1294440, 3014775, 6946951, 15859864, 35913898, 80740541, 180355281, 400556262, 884998396, 1946157331, 4261413163, 9294577988, 20199768414, 43754979705, 94489280917, 203474076082
OFFSET
1,2
FORMULA
G.f.: x*(1 - 7*x + 21*x^2 - 30*x^3 + 22*x^4 - 8*x^5) / ((1 - x)^3*(1 - 2*x)^3).
From Colin Barker, Oct 30 2017: (Start)
a(n) = (1/4)*(-4 + 2^(3+n) - (2+5*2^n)*n + (2+2^n)*n^2).
a(n) = 9*a(n-1) - 33*a(n-2) + 63*a(n-3) - 66*a(n-4) + 36*a(n-5) - 8*a(n-6) for n>6.
(End)
PROG
(PARI) Vec(x*(1 - 7*x + 21*x^2 - 30*x^3 + 22*x^4 - 8*x^5) / ((1 - x)^3*(1 - 2*x)^3) + O(x^40)) \\ Colin Barker, Oct 30 2017
CROSSREFS
Sequence in context: A294798 A294799 A294693 * A116839 A294800 A116776
KEYWORD
nonn,easy
AUTHOR
Lara Pudwell, Feb 26 2006
STATUS
approved