A158762 Expansion of (1+9*x+80*x^2)/(1-x^2-729*x^3).

1, 9, 81, 738, 6642, 59787, 544644, 4901805, 44129367, 401947281, 3617545212, 32572255824, 296637113061, 2669762715372, 24041811608757, 218918218136841, 1970298831114945, 17745398880920694, 161561679852872034

Offset

0,2

Comments

This can be generated by multiplying the sum of the elements in the top row of the n-th power of the matrix [(0,3,0), (0,0,3),(3,1/27,0)] by 3^n.

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,1,729).

Formula

a(n)=a(n-2)+729*a(n-3). [From R. J. Mathar, Mar 26 2009]

Mathematica

Clear[M, v, t, n];
M = {{0, t, 0}, {0, 0, t}, {t, 1/t^3, 0}};
v[0] = {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}]

Crossrefs

Sequence in context: A047901 A061587 A033145 * A101601 A233737 A344298

Adjacent sequences: A158759 A158760 A158761 * A158763 A158764 A158765

Keyword

nonn

Author

Roger L. Bagula, Mar 25 2009

Status

approved