A080881 a(n)*a(n+3) - a(n+1)*a(n+2) = 2^n, given a(0)=1, a(1)=2, a(2)=10.

1, 2, 10, 21, 106, 223, 1126, 2369, 11962, 25167, 127078, 267361, 1350010, 2840303, 14341798, 30173889, 152359738, 320551567, 1618589926, 3405371681, 17195050234, 36176882223, 182671192870, 384324217729, 1940602920634

Offset

0,2

Links

Table of n, a(n) for n=0..24.

Formula

G.f.: (-x^3 - x^2 + 2*x + 1)/(4*x^4 - 11*x^2 + 1)

a(n + 4) = 11*a(n + 2) - 4*a(n) [From Richard Choulet, Dec 06 2008]

a(n) = (3/140*15^(1/2)*7^(1/2) + 1/4 + 3/56*7^(1/2) + 1/24*15^(1/2))*sqrt((11 + sqrt(105))/2)^n + ( - 3/140*15^(1/2)*7^(1/2) + 1/4 - 3/56*7^(1/2) + 1/24*15^(1/2))*sqrt((11 - sqrt(105))/2)^n + (3/140*15^(1/2)*7^(1/2) - 1/24*15^(1/2) - 3/56*7^(1/2) + 1/4)*( - sqrt((11 + sqrt(105))/2))^n + (1/4 + 3/56*7^(1/2) - 1/24*15^(1/2) - 3/140*15^(1/2)*7^(1/2))*( - sqrt((11 - sqrt(105))/2))^n [From Richard Choulet, Dec 07 2008]

Crossrefs

Cf. A080876, A080877, A080878, A080879, A080880, A080882.

Sequence in context: A304700 A318548 A318210 * A138298 A303294 A302566

Adjacent sequences: A080878 A080879 A080880 * A080882 A080883 A080884

Keyword

nonn

Author

Paul D. Hanna, Feb 22 2003

Status

approved