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%I #29 Dec 26 2022 06:08:27
%S 0,1,1,2,3,21,50,161,501,1532,4723,14551,44800,137971,424901,1308512,
%T 4029693,12409831,38217250,117693681,362448951,1116196192,3437432913,
%U 10585903361,32600301650,100395746291,309178300901,952144142322,2932218933633
%N a(n) = a(n-1) + 4*a(n-2) + 6*a(n-3) + 4*a(n-4) + a(n-5).
%H Harvey P. Dale, <a href="/A114749/b114749.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,4,6,4,1).
%F G.f.: x*(9*x^3 + 3*x^2 - 1)/((x^2 + x + 1)*(x^3 + 3*x^2 + 2*x - 1)). [Maksym Voznyy (voznyy(AT)mail.ru), Aug 12 2009]
%t LinearRecurrence[{1,4,6,4,1},{0,1,1,2,3},30] (* _Harvey P. Dale_, Oct 13 2011 *)
%o (PARI) x='x+O('x^50); concat([0], Vec(x*(9*x^3+3*x^2-1)/((x^2+x+1)*(x^3+ 3*x^2+2*x-1)))) \\ G. C. Greubel, Nov 03 2018
%o (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!(x*(9*x^3+3*x^2-1)/((x^2+x+1)*(x^3+ 3*x^2+2*x-1)))); // G. C. Greubel, Nov 03 2018
%Y Cf. A107479, A107480, A109538, A109543, A109544, A125950, A130844, A143335, A147851.
%K nonn,easy
%O 0,4
%A _Roger L. Bagula_, Feb 18 2006
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