OFFSET
0,3
COMMENTS
a(n) is the number of permutations of length n avoiding the partially ordered pattern (POP) {1>5} of length 5. That is, the number of length n permutations having no subsequences of length 5 in which the first element is larger than the fifth element. - Sergey Kitaev, Dec 11 2020
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
Alice L. L. Gao, Sergey Kitaev, On partially ordered patterns of length 4 and 5 in permutations, arXiv:1903.08946 [math.CO], 2019.
Alice L. L. Gao, Sergey Kitaev, On partially ordered patterns of length 4 and 5 in permutations, The Electronic Journal of Combinatorics 26(3) (2019), P3.26.
Index entries for linear recurrences with constant coefficients, signature (1,2,2,12,8,-2,-5,-1).
FORMULA
G.f.: -(x-1)*(x+1)/(x^8+5*x^7+2*x^6-8*x^5-12*x^4-2*x^3-2*x^2-x+1).
MATHEMATICA
CoefficientList[Series[-(x - 1) (x + 1)/(x^8 + 5 x^7 + 2 x^6 - 8 x^5 - 12 x^4 - 2 x^3 - 2 x^2 - x + 1), {x, 0, 29}], x] (* Michael De Vlieger, Oct 14 2017 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Sep 20 2016
STATUS
approved