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A276838
Number of permutations of [n] such that for each cycle c the smallest integer interval containing all elements of c has at most four elements.
3
1, 1, 2, 6, 24, 60, 150, 399, 1145, 3132, 8420, 22716, 62128, 169536, 460885, 1251777, 3406238, 9272354, 25229036, 68622196, 186682470, 507925571, 1381929921, 3759616968, 10228269080, 27827267544, 75707898304, 205971928848, 560368255081, 1524544463441
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
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.
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
Column k=4 of A276837.
Cf. A276720.
Sequence in context: A289161 A118038 A240428 * A364424 A022917 A189855
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Sep 20 2016
STATUS
approved