A136786 Number of primitive multiplex juggling sequences of length n, base state <2,1> and hand capacity 3.

1, 4, 21, 111, 592, 3171, 17021, 91456, 491641, 2643523, 14215596, 76448559, 411134641, 2211076788, 11891207045, 63951270079, 343932277888, 1849681481203, 9947663349453, 53498950981392, 287719621233865, 1547368337500659, 8321812723167356, 44755063012476127

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..1000

S. Butler and R. Graham, Enumerating (multiplex) juggling sequences, arXiv:0801.2597 [math.CO], 2008.

Index entries for linear recurrences with constant coefficients, signature (9,-22,13,3).

Formula

G.f.: (x-5*x^2+7*x^3-3*x^4)/(1-9*x+22*x^2-13*x^3-3*x^4).

a(n) = 9*a(n-1)-22*a(n-2)+13*a(n-3)+3*a(n-4) for n>4. - Colin Barker, Aug 31 2016

Mathematica

LinearRecurrence[{9, -22, 13, 3}, {1, 4, 21, 111}, 30] (* Harvey P. Dale, Feb 13 2022 *)

Prog

(PARI) Vec((x-5*x^2+7*x^3-3*x^4)/(1-9*x+22*x^2-13*x^3-3*x^4) + O(x^30)) \\ Colin Barker, Aug 31 2016

Crossrefs

Cf. A136785.

Sequence in context: A100237 A117381 A010908 * A301972 A026335 A027909

Adjacent sequences: A136783 A136784 A136785 * A136787 A136788 A136789

Keyword

nonn,easy

Author

Steve Butler, Jan 21 2008

Status

approved