A080879 a(n)*a(n+3) - a(n+1)*a(n+2) = 2^n, given a(0)=1, a(1)=1, a(2)=6.

1, 1, 6, 7, 44, 52, 328, 388, 2448, 2896, 18272, 21616, 136384, 161344, 1017984, 1204288, 7598336, 8988928, 56714752, 67094272, 423324672, 500798464, 3159738368, 3738010624, 23584608256, 27900891136, 176037912576, 208255086592, 1313964867584, 1554437128192

Offset: 0

Author

Paul D. Hanna, Feb 22 2003

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,8,0,-4).

Crossrefs

Cf. A080876, A080877, A080878, A080880, A080881, A080882.

Programs

Maple

a:= n-> (<<0|1>, <-4|8>>^floor(n/2). <<1, 6+(n mod 2)>>)[1,1]:
seq(a(n), n=0..30);  # Alois P. Heinz, Mar 18 2023

Mathematica

LinearRecurrence[{0,8,0,-4},{1,1,6,7},30] (* Harvey P. Dale, Mar 10 2015 *)

Formula

a(2n) = A080876(2n+3)/2, a(2n+1) = A080876(2n+4)/4.

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

a(n) = ((9/16)*sqrt(3) - 7/16)*(1 + sqrt(3))^n + (-(9/16)*sqrt(3) - 7/16)*(1 - sqrt(3))^n + (-(19/48)*sqrt(3) + 15/16)*(-(1 + sqrt(3)))^n + ((19/48)*sqrt(3) + 15/16)*(-(1 - sqrt(3)))^n. - Richard Choulet, Dec 06 2008

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