%I #10 Apr 05 2019 17:22:12

%S 1,4,16,72,288,1168,5184,20768,85120,373312,1499392,6194304,26890752,

%T 108349696,450216960,1937707520,7834814464,32689300480,139682910208,

%U 566806726656,2371481051136,10073319706624,41018592608256

%N Expansion of (1+4*x+14*x^2)/(1-2*x^2-64*x^3).

%C Can be generated by multiplying the sum of the top row of the n-th power of the matrix [ (0,2,0), (0,0,2), (2,1/4,0)] by 2^n.

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,64).

%F a(n)= 2*a(n-2) +64*a(n-3). [From R. J. Mathar, Mar 31 2009]

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

%t M = {{0, t, 0}, {0, 0, t}, {t, 1/t^2, 0}};

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

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

%t CharacteristicPolynomial[M, x];

%t t = 2;

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

%t LinearRecurrence[{0,2,64},{1,4,16},30] (* _Harvey P. Dale_, Apr 05 2019 *)

%K nonn

%O 0,2

%A _Roger L. Bagula_, Mar 26 2009