A098992 Number of permutations of [n] with exactly 2 descents which avoid the pattern 1324.
0, 0, 1, 11, 55, 190, 526, 1254, 2682, 5280, 9735, 17017, 28457, 45838, 71500, 108460, 160548, 232560, 330429, 461415, 634315, 859694, 1150138, 1520530, 1988350, 2574000, 3301155, 4197141, 5293341, 6625630, 8234840, 10167256, 12475144, 15217312, 18459705
Offset: 1
Links
- Colin Barker, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).
Programs
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PARI
concat(vector(2), Vec(x^3*(1 + 3*x - 5*x^2 + 2*x^3) / (1 - x)^8 + O(x^30))) \\ Colin Barker, Oct 26 2017
Formula
G.f.: x^3*(1 + 3*x - 5*x^2 + 2*x^3) / (1 - x)^8.
From Colin Barker, Oct 26 2017: (Start)
a(n) = (n*(-540 + 476*n + 469*n^2 - 490*n^3 + 70*n^4 + 14*n^5 + n^6)) / 5040.
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
(End)