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

%I #9 Feb 13 2022 16:04:40

%S 1,4,21,111,592,3171,17021,91456,491641,2643523,14215596,76448559,

%T 411134641,2211076788,11891207045,63951270079,343932277888,

%U 1849681481203,9947663349453,53498950981392,287719621233865,1547368337500659,8321812723167356,44755063012476127

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

%H Colin Barker, <a href="/A136786/b136786.txt">Table of n, a(n) for n = 1..1000</a>

%H S. Butler and R. Graham, <a href="http://arXiv.org/abs/0801.2597">Enumerating (multiplex) juggling sequences</a>, arXiv:0801.2597 [math.CO], 2008.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (9,-22,13,3).

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

%F 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

%t LinearRecurrence[{9,-22,13,3},{1,4,21,111},30] (* _Harvey P. Dale_, Feb 13 2022 *)

%o (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

%Y Cf. A136785.

%K nonn,easy

%O 1,2

%A _Steve Butler_, Jan 21 2008