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%I #28 Mar 09 2022 15:52:30
%S 1,1,2,6,24,118,644,3622,20366,113686,630464,3481084,19171838,
%T 105444400,579547826,3184321642,17493771830,96100287256,527905628552,
%U 2899911094078,15929870658308,87506389326742,480692570563526,2640554790693958,14505177373598504
%N The number of permutations of length n that can be sorted by 3 pop stacks in parallel.
%H Colin Barker, <a href="/A164871/b164871.txt">Table of n, a(n) for n = 0..1000</a>
%H R. Smith and V. Vatter, <a href="https://www.semanticscholar.org/paper/The-enumeration-of-permutations-sortable-by-pop-in-Smith-Vatter/653c589cffdddc1f6964e1741574742cc7b00546">The enumeration of permutations sortable by pop stacks in parallel</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (14,-75,201,-288,216,-72).
%F G.f.: (1 -13*x +63*x^2 -148*x^3 +177*x^4 -98*x^5 +18*x^6) / (1 -14*x +75*x^2 -201*x^3 +288*x^4 -216*x^5 +72*x^6).
%F a(n) = 14*a(n-1) - 75*a(n-2) + 201*a(n-3) - 288*a(n-4) + 216*a(n-5) - 72*a(n-6) for n>6. - _Colin Barker_, Jul 02 2019
%t LinearRecurrence[{14,-75,201,-288,216,-72},{1,1,2,6,24,118,644},30] (* _Harvey P. Dale_, Mar 09 2022 *)
%o (PARI) Vec((1 - x)*(1 - 12*x + 51*x^2 - 97*x^3 + 80*x^4 - 18*x^5) / ((1 - 2*x)*(1 - 12*x + 51*x^2 - 99*x^3 + 90*x^4 - 36*x^5)) + O(x^30)) \\ _Colin Barker_, Jul 02 2019
%K nonn,easy
%O 0,3
%A _Vincent Vatter_, Aug 29 2009
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