OFFSET
0,2
COMMENTS
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.
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,0,0,6561).
FORMULA
a(n)= a(n-1)+6561*a(n-4). [From R. J. Mathar, Mar 31 2009]
MATHEMATICA
Clear[M, v, t, n];
M = {{0, t, 0, 0}, {0, 0, t, 0}, {0, 0, 0, t}, {t, 0, 0, 1/t}};
v[0] = {1, 1, 1, 1};
v[n_] := v[n] = M.v[n - 1];
CharacteristicPolynomial[M, x];
t = 3;
a = Table[t^n*v[n][[1]], {n, 0, 30}]
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Mar 26 2009
STATUS
approved