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A116850
Number of permutations of length n which avoid the patterns 231, 12354.
1
1, 2, 5, 14, 41, 119, 334, 902, 2351, 5945, 14660, 35408, 84061, 196715, 454778, 1040522, 2359451, 5308589, 11862208, 26345684, 58196201, 127926527, 279970070, 610271534, 1325400391, 2868904289, 6190793084, 13321109912, 28588376501, 61203284435, 130728067570
OFFSET
1,2
COMMENTS
Inverse binomial transform (offset 0) is: 0, 1, 0, 2, 2, 6, 7, 12, 14, 20, 23, 30, 34, 42, 47, 56, 62, 72,.. with difference pattern +1, -1, +2, +0, +4, +1, +5, +2, +6, +3,... as in A168230. - R. J. Mathar, Feb 23 2013
FORMULA
G.f.: x*(1 - 7*x + 20*x^2 - 28*x^3 + 20*x^4 - 7*x^5) / ((1 - x)^3*(1 - 2*x)^3).
From Colin Barker, Oct 30 2017: (Start)
a(n) = (1/16)*(32-9*2^(1+n) + (8+2^n)*n + (8+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 + 20*x^2 - 28*x^3 + 20*x^4 - 7*x^5) / ((1 - x)^3*(1 - 2*x)^3) + O(x^40)) \\ Colin Barker, Oct 30 2017
CROSSREFS
Sequence in context: A116844 A116851 A038989 * A116847 A116848 A370800
KEYWORD
nonn,easy
AUTHOR
Lara Pudwell, Feb 26 2006
STATUS
approved