A158779 - OEIS

%I #9 Jun 19 2015 11:19:42

%S 1,9,81,729,7290,66339,597780,5380749,53210439,488460618,4410495198,

%T 39713589387,388827279666,3593617394364,32530876388442,

%U 293091736356549,2844187518245175,26421911242667379,239856991227235341

%N Expansion of (1+8*x+72*x^2+648*x^3)/(1-x-6561*x^4).

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

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,6561).

%F a(n)= a(n-1)+6561*a(n-4). [From R. J. Mathar, Mar 31 2009]

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

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

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

%t CoefficientList[Series[(1+8x+72x^2+648x^3)/(1-x-6561x^4),{x,0,20}],x] (* or *) LinearRecurrence[{1,0,0,6561},{1,9,81,729},20] (* _Harvey P. Dale_, Jun 18 2015 *)

%K nonn

%O 0,2

%A _Roger L. Bagula_, Mar 26 2009