A080875 a(n)*a(n+3) - a(n+1)*a(n+2) = 5, given a(0)=a(1)=1, a(2)=6.

1, 1, 6, 11, 71, 131, 846, 1561, 10081, 18601, 120126, 221651, 1431431, 2641211, 17057046, 31472881, 203253121, 375033361, 2421980406, 4468927451, 28860511751, 53252096051, 343904160606, 634556225161, 4097989415521

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1500

Index entries for linear recurrences with constant coefficients, signature (0, 12, 0, -1).

Formula

G.f.: (-x^3 - 6*x^2 + x + 1)/(x^4 - 12*x^2 + 1).

a(n+4) = 12*a(n+2)-a(n). - Richard Choulet, Dec 04 2008

a(n) = (1/4 + ((sqrt(6 + sqrt(35)) - sqrt(6 - sqrt(35)))/(4*sqrt(35))))*(sqrt(6 + sqrt(35)))^n + (1/4 + ((sqrt(6 + sqrt(35)) - sqrt(6 - sqrt(35)))/(4*sqrt(35))))*(sqrt(6 - sqrt(35)))^n + (1/4 - ((sqrt(6 + sqrt(35)) - sqrt(6 - sqrt(35)))/(4*sqrt(35))))*( - sqrt(6 + sqrt(35)))^n + (1/4 - ((sqrt(6 + sqrt(35)) - sqrt(6 - sqrt(35)))/(4*sqrt(35))))*( - (sqrt(6 - sqrt(35))))^n. - Richard Choulet, Dec 06 2008

Mathematica

LinearRecurrence[{0, 12, 0, -1}, {1, 1, 6, 11}, 30] (* Harvey P. Dale, Jul 14 2024 *)

Prog

(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; -1, 0, 12, 0]^n*[1; 1; 6; 11])[1, 1] \\ Charles R Greathouse IV, May 16 2026

Crossrefs

Cf. A080871, A080872, A080873, A080874.

Bisections are A023038 and A077417.

Sequence in context: A128387 A061519 A193664 * A001543 A077705 A077697

Adjacent sequences: A080872 A080873 A080874 * A080876 A080877 A080878

Keyword

nonn,easy

Author

Paul D. Hanna, Feb 22 2003

Status

approved