A080880 a(n)*a(n+3) - a(n+1)*a(n+2) = 2^n, given a(0)=1, a(1)=2, a(2)=2.

1, 2, 2, 5, 6, 17, 22, 65, 86, 257, 342, 1025, 1366, 4097, 5462, 16385, 21846, 65537, 87382, 262145, 349526, 1048577, 1398102, 4194305, 5592406, 16777217, 22369622, 67108865, 89478486, 268435457, 357913942, 1073741825, 1431655766, 4294967297

Offset: 0

Author

Paul D. Hanna, Feb 22 2003

Keywords

• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (0, 5, 0, -4).

Crossrefs

Cf. A080876, A080877, A080878, A080879, A080881, A080882.

Programs

Mathematica

LinearRecurrence[{0,5,0,-4},{1,2,2,5},40] (* Harvey P. Dale, Nov 30 2012 *)

Formula

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

G.f.: (-5*x^3 - 3*x^2 + 2*x + 1)/(4*x^4 - 5*x^2 + 1)

a(n) = 5/6 + 5/12*2^n - 1/6*( - 1)^n - 1/12*( - 2)^n [From Richard Choulet, Dec 07 2008]

a(n + 4) = 5*a(n + 2) - 4*a(n) [From Richard Choulet, Dec 06 2008]

Extensions

More terms from Ralf Stephan, Jul 25 2003