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Expansion of (1+8*x)/(1-x-81*x^2).
2

%I #18 Jan 01 2024 08:34:22

%S 1,9,90,819,8109,74448,731277,6761565,65995002,613681767,5959276929,

%T 55667500056,538368931305,5047436435841,48655319871546,

%U 457497671174667,4398578580769893,41455889945917920,397740754988279253

%N Expansion of (1+8*x)/(1-x-81*x^2).

%D H. S. M. Coxeter, Regular Polytopes, 3rd ed., Dover, NY, 1973, page 221.

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (1,81).

%F a(n) = a(n-1) + 81*a(n-2), a(0)=1, a(1)=9. - _Philippe Deléham_, Mar 26 2009

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

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

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

%t t = 3;

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

%K nonn,easy

%O 0,2

%A _Roger L. Bagula_, Mar 22 2009

%E Clearer definition from _Philippe Deléham_, Mar 26 2009