OFFSET
0,3
COMMENTS
Also the number of permutations that are sortable after two passes through a pop stack. (See the Pudwell-Smith link.) - Lara Pudwell, Jun 01 2017
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
G. Aleksandrowich et al., Permutations with forbidden patterns and polyominoes on a twisted cylinder of width 3, Discrete Math., 313 (2013), 1078-1086.
Anders Claesson and Bjarki Ágúst Guðmundsson, Enumerating permutations sortable by k passes through a pop-stack, arXiv:1710.04978 [math.CO], 2017.
Lara Pudwell and Rebecca Smith, Sorting with Pop Stacks, Special Session on Algebraic and Enumerative Combinatorics with Applications, AMS Central Section Spring Meeting, 2017.
Lara Pudwell and Rebecca Smith, Two-stack-sorting with pop stacks, arXiv:1801.05005 [math.CO], 2018.
Index entries for linear recurrences with constant coefficients, signature (2,1,2).
FORMULA
G.f.: (x^3 + x^2 + x - 1) / (2*x^3 + x^2 + 2*x - 1). - Colin Barker, Jun 07 2015
a(n) = (b(n) + b(n-1))/2 for b(n) = A077996(n). - Hanzhang Fang, Aug 27 2022
MATHEMATICA
CoefficientList[Series[(x^3 + x^2 + x - 1)/(2 x^3 + x^2 + 2 x - 1), {x, 0, 35}], x] (* Michael De Vlieger, Jun 01 2017 *)
LinearRecurrence[{2, 1, 2}, {1, 1, 2, 6}, 40] (* Harvey P. Dale, Aug 28 2023 *)
PROG
(PARI) Vec((x^3+x^2+x-1)/(2*x^3+x^2+2*x-1) + O(x^100)) \\ Colin Barker, Jun 07 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Apr 11 2013
STATUS
approved