A080876 a(n)*a(n+3) - a(n+1)*a(n+2) = 2^n, given a(0) = 1, a(1) = 1, and a(2) = 1.

1, 1, 1, 2, 4, 12, 28, 88, 208, 656, 1552, 4896, 11584, 36544, 86464, 272768, 645376, 2035968, 4817152, 15196672, 35955712, 113429504, 268377088, 846649344, 2003193856, 6319476736, 14952042496, 47169216512, 111603564544

Offset

0,4

Links

Table of n, a(n) for n=0..28.

Formula

G.f.: (-6*x^3 - 7*x^2 + x + 1)/(4*x^4 - 8*x^2 + 1)

a(n + 4) = 8*a(n + 2) - 4*a(n). - Richard Choulet, Dec 06 2008

a(n) = (1/24 * 3^(1/2)) * (1 + sqrt(3))^n - (1/24 * 3^(1/2)) * (1 - sqrt(3))^n + (1/2 - 7/24 * 3^(1/2)) * (-(1 + sqrt(3)))^n + (1/2 + 7/24 * 3^(1/2))*(-(1 - sqrt(3)))^n. - Richard Choulet, Dec 06 2008

Mathematica

CoefficientList[Series[(-6x^3-7x^2+x+1)/(4x^4-8x^2+1), {x, 0, 40}], x]  (* Harvey P. Dale, Mar 04 2011 *)

Crossrefs

Cf. A080871, A080877, A080878, A080879, A080880, A080881, A080882.

Sequence in context: A148175 A148176 A148177 * A148178 A148179 A148180

Adjacent sequences: A080873 A080874 A080875 * A080877 A080878 A080879

Keyword

nonn

Author

Paul D. Hanna, Feb 22 2003

Status

approved