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A164870
The number of permutations of length n that can be sorted by 2 pop stacks in parallel.
2
1, 2, 6, 22, 84, 320, 1212, 4576, 17256, 65048, 245184, 924160, 3483408, 13129952, 49490592, 186544480, 703140672, 2650342784, 9989916864, 37654917376, 141932392320, 534984681344, 2016513669120, 7600829555200, 28649748728064, 107989278831104, 407043163037184
OFFSET
1,2
LINKS
Anders Claesson, Mark Dukes and Martina Kubitzke, Partition and composition matrices, arXiv:1006.1312 [math.CO], 2010-2011.
R. Smith and V. Vatter, The enumeration of permutations sortable by pop stacks in parallel, Information Processing Letters, Volume 109, Issue 12, 31 May 2009, Pages 626-629.
FORMULA
G.f.: -x*(2*x-1)^2 / ( -1+6*x-10*x^2+6*x^3 ).
a(n) = 6*a(n-1) - 10*a(n-2) + 6*a(n-3) for n>3. - Colin Barker, Oct 31 2017
MATHEMATICA
LinearRecurrence[{6, -10, 6}, {1, 2, 6}, 30] (* Harvey P. Dale, Oct 12 2023 *)
PROG
(PARI) Vec(x*(1 - 2*x)^2 / (1 - 6*x + 10*x^2 - 6*x^3) + O(x^30)) \\ Colin Barker, Oct 31 2017
CROSSREFS
Sequence in context: A150242 A150243 A200316 * A121686 A245904 A128723
KEYWORD
nonn,easy
AUTHOR
Vincent Vatter, Aug 29 2009
STATUS
approved

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