A158779 Expansion of (1+8*x+72*x^2+648*x^3)/(1-x-6561*x^4).

1, 9, 81, 729, 7290, 66339, 597780, 5380749, 53210439, 488460618, 4410495198, 39713589387, 388827279666, 3593617394364, 32530876388442, 293091736356549, 2844187518245175, 26421911242667379, 239856991227235341

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

Table of n, a(n) for n=0..18.

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

Sequence in context: A074118 A050739 A240945 * A047901 A061587 A033145

Adjacent sequences: A158776 A158777 A158778 * A158780 A158781 A158782

Keyword

nonn

Author

Roger L. Bagula, Mar 26 2009

Status

approved