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A158762 Expansion of (1+9*x+80*x^2)/(1-x^2-729*x^3). 0

%I

%S 1,9,81,738,6642,59787,544644,4901805,44129367,401947281,3617545212,

%T 32572255824,296637113061,2669762715372,24041811608757,

%U 218918218136841,1970298831114945,17745398880920694,161561679852872034

%N Expansion of (1+9*x+80*x^2)/(1-x^2-729*x^3).

%C This can be generated by multiplying the sum of the elements in the top row of the n-th power of the matrix [(0,3,0), (0,0,3),(3,1/27,0)] by 3^n.

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,729).

%F a(n)=a(n-2)+729*a(n-3). [From R. J. Mathar, Mar 26 2009]

%t Clear[M, v, t, n];

%t M = {{0, t, 0}, {0, 0, t}, {t, 1/t^3, 0}};

%t v[0] = {1, 1, 1};

%t v[n_] := v[n] = M.v[n - 1];

%t CharacteristicPolynomial[M, x];

%t t = 3;

%t a = Table[t^n*v[n][[1]], {n, 0, 30}]

%K nonn

%O 0,2

%A _Roger L. Bagula_, Mar 25 2009

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Last modified July 25 18:20 EDT 2021. Contains 346291 sequences. (Running on oeis4.)