A080874 a(n)*a(n+3) - a(n+1)*a(n+2) = 5, given a(0)=a(1)=1, a(2)=3.

1, 1, 3, 8, 29, 79, 287, 782, 2841, 7741, 28123, 76628, 278389, 758539, 2755767, 7508762, 27279281, 74329081, 270037043, 735782048, 2673091149, 7283491399, 26460874447, 72099131942, 261935653321, 713707828021, 2592895658763

Offset: 0

Author

Paul D. Hanna, Feb 22 2003

Keywords

• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (0,10,0,-1).

Crossrefs

Cf. A080871, A080872, A080873, A080875.

Programs

Mathematica

LinearRecurrence[{0,10,0,-1},{1,1,3,8},30] (* Harvey P. Dale, Sep 18 2016 *)

Formula

G.f.: (1+x-7x^2-2x^3)/(1-10x^2+x^4). a(n)=10a(n-2)-a(n-4). - Michael Somos, Mar 04 2003.

a(n) = ( - 1/24*3^(1/2)*2^(1/2) + 1/4 - 1/16*2^(1/2) + 1/8*3^(1/2))*(sqrt(3) + sqrt(2))^n + (1/24*3^(1/2)*2^(1/2) + 1/4 + 1/16*2^(1/2) + 1/8*3^(1/2))*(sqrt(3) - sqrt(2))^n + ( - 1/24*3^(1/2)*2^(1/2) - 1/8*3^(1/2) + 1/16*2^(1/2) + 1/4)*( - sqrt(3) - sqrt(2))^n + ( - 1/16*2^(1/2) + 1/4 + 1/24*3^(1/2)*2^(1/2) - 1/8*3^(1/2))*( - sqrt(3) + sqrt(2))^n [From Richard Choulet, Dec 04 2008]