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A136775
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Number of multiplex juggling sequences of length n, base state <1,1> and hand capacity 2.
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3
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1, 3, 11, 40, 145, 525, 1900, 6875, 24875, 90000, 325625, 1178125, 4262500, 15421875, 55796875, 201875000, 730390625, 2642578125, 9560937500, 34591796875, 125154296875, 452812500000, 1638291015625, 5927392578125, 21445507812500, 77590576171875
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OFFSET
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1,2
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COMMENTS
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Except for the initial 1, this is the p-INVERT of (1,1,1,1,1,...) for p(S) = 1 - 3 S + S^2; see A291000. - Clark Kimberling, Aug 24 2017
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LINKS
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FORMULA
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G.f.: (x-2x^2+x^3)/(1-5x+5x^2).
a(n) = 5*a(n-1)-5*a(n-2) for n>3. - Colin Barker, Aug 31 2016
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MATHEMATICA
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CoefficientList[Series[(x^2-2x+1)/(5x^2-5x+1), {x, 0, 30}], x] (* Harvey P. Dale, Jun 22 2014 *)
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PROG
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(PARI) Vec((x-2*x^2+x^3)/(1-5*x+5*x^2) + O(x^30)) \\ Colin Barker, Aug 31 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 27); Coefficients(R!( (x-2*x^2+x^3)/(1-5*x+5*x^2))); // Marius A. Burtea, Jan 13 2020
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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