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

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 (0,11,0,-4).

Crossrefs

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

Programs

Mathematica

CoefficientList[Series[(-x^3-x^2+2x+1)/(4x^4-11x^2+1),{x,0,30}],x] (* or *) LinearRecurrence[ {0,11,0,-4},{1,2,10,21},30] (* Harvey P. Dale, Jun 10 2024 *)

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]