A171590 a(n) = 1+4^(n+1)-4*(-2)^n.

1, 25, 49, 289, 961, 4225, 16129, 66049, 261121, 1050625, 4190209, 16785409, 67092481, 268468225, 1073676289, 4295098369, 17179607041, 68720001025, 274876858369, 1099513724929, 4398042316801, 17592194433025, 70368727400449

Offset: 0

Author

R. J. Mathar, Dec 12 2009

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,6,-8).

Programs

Magma

I:=[1, 25, 49]; [n le 3 select I[n] else 3*Self(n-1) + 6*Self(n-2) - 8*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Dec 19 2012

Mathematica

CoefficientList[Series[(1 + 22*x - 32*x^2)/((x - 1)*(2*x + 1)*(4*x-1)), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 19 2012 *)

Formula

a(n) = A105951(2n+1) = (A014551(n+1))^2.

G.f.: (1+22*x-32*x^2)/((x-1)*(2*x+1)*(4*x-1)).

a(n) = 3*a(n-1)+6*a(n-2)-8*a(n-3).

Extensions

G.f. Adapted by Vincenzo Librandi, Dec 19 2012