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Expansion of x*(1+x+2*x^3) / ((x-1)*(1+x)*(3*x^2-1)).
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%I #19 Dec 29 2023 10:59:37

%S 0,1,1,4,6,13,21,40,66,121,201,364,606,1093,1821,3280,5466,9841,16401,

%T 29524,49206,88573,147621,265720,442866,797161,1328601,2391484,

%U 3985806,7174453,11957421,21523360,35872266,64570081,107616801,193710244

%N Expansion of x*(1+x+2*x^3) / ((x-1)*(1+x)*(3*x^2-1)).

%C Top element of the vector obtained by multiplying the n-th power of the 5 X 5 matrix [[0, 1, 0, 0, 0], [1, 0, 1, 0, 0], [0, 1, 0, 1, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0]] by the column vector [0, 1, 1, 2, 3].

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,4,0,-3).

%F G.f.: x*(1+x+2*x^3) / ((x-1)*(1+x)*(3*x^2-1)).

%F a(2n+2) = A134931(n). a(2n+1) = A003462(n+1). - _R. J. Mathar_, Nov 07 2011

%t LinearRecurrence[{0,4,0,-3},{0,1,1,4,6},40] (* _Harvey P. Dale_, Dec 15 2018 *)

%Y Cf. A003462, A134931.

%K nonn,easy

%O 0,4

%A _Roger L. Bagula_ and _Gary W. Adamson_, Jun 30 2006