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A164871
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The number of permutations of length n that can be sorted by 3 pop stacks in parallel.
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1
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1, 1, 2, 6, 24, 118, 644, 3622, 20366, 113686, 630464, 3481084, 19171838, 105444400, 579547826, 3184321642, 17493771830, 96100287256, 527905628552, 2899911094078, 15929870658308, 87506389326742, 480692570563526, 2640554790693958, 14505177373598504
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OFFSET
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0,3
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LINKS
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Colin Barker, Table of n, a(n) for n = 0..1000
R. Smith and V. Vatter, The enumeration of permutations sortable by pop stacks in parallel
Index entries for linear recurrences with constant coefficients, signature (14,-75,201,-288,216,-72).
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FORMULA
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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).
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
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MATHEMATICA
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LinearRecurrence[{14, -75, 201, -288, 216, -72}, {1, 1, 2, 6, 24, 118, 644}, 30] (* Harvey P. Dale, Mar 09 2022 *)
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PROG
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(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
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CROSSREFS
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Sequence in context: A177518 A319027 A228397 * A226436 A224318 A079106
Adjacent sequences: A164868 A164869 A164870 * A164872 A164873 A164874
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KEYWORD
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nonn,easy
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AUTHOR
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Vincent Vatter, Aug 29 2009
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STATUS
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approved
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