A293774 Number of permutations of length n sortable by 3 passes through a pop-stack.

1, 1, 2, 6, 24, 88, 303, 1033, 3544, 12220, 42164, 145364, 500954, 1726408, 5950050, 20507364, 70680192, 243602952, 839588620, 2893682172, 9973219220, 34373198420, 118468937648, 408309065104, 1407257423576, 4850182474912

Offset: 0

Author

Bjarki Ágúst Guðmundsson, Oct 16 2017

Keywords

• nonn
• easy

Links

• Bjarki Ágúst Guðmundsson, Table of n, a(n) for n = 0..1000
• Anders Claesson, Bjarki Ágúst Guðmundsson, Enumerating permutations sortable by k passes through a pop-stack, arXiv:1710.04978 [math.CO], 2017.

Crossrefs

Cf. A224232, A293775, A293776, A293784.

Programs

PARI

Vec((2*x^10 + 4*x^9 + 2*x^8 + 5*x^7 + 11*x^6 + 8*x^5 + 6*x^4 + 6*x^3 + 2*x^2 + x - 1)/(4*x^10 + 8*x^9 + 4*x^8 + 10*x^7 + 22*x^6 + 16*x^5 + 8*x^4 + 6*x^3 + 2*x^2 + 2*x - 1) + O(x^30))

Formula

G.f.: (2*x^10 + 4*x^9 + 2*x^8 + 5*x^7 + 11*x^6 + 8*x^5 + 6*x^4 + 6*x^3 + 2*x^2 + x - 1) / (4*x^10 + 8*x^9 + 4*x^8 + 10*x^7 + 22*x^6 + 16*x^5 + 8*x^4 + 6*x^3 + 2*x^2 + 2*x - 1).