A158609 Expansion of (1+8*x)/(1-x-81*x^2).

1, 9, 90, 819, 8109, 74448, 731277, 6761565, 65995002, 613681767, 5959276929, 55667500056, 538368931305, 5047436435841, 48655319871546, 457497671174667, 4398578580769893, 41455889945917920, 397740754988279253

Offset: 0

Author

Roger L. Bagula, Mar 22 2009

Keywords

• nonn
• easy

References

• H. S. M. Coxeter, Regular Polytopes, 3rd ed., Dover, NY, 1973, page 221.

Links

• Index entries for linear recurrences with constant coefficients, signature (1,81).

Programs

Mathematica

M = {{0, t}, {t, 1/t}};
v[0] = {1, 1};
v[n_] := v[n] = M.v[n - 1];
t = 3;
a = Table[t^n*v[n][[1]], {n, 0, 30}]

Formula

a(n) = a(n-1) + 81*a(n-2), a(0)=1, a(1)=9. - Philippe Deléham, Mar 26 2009

Extensions

Clearer definition from Philippe Deléham, Mar 26 2009