OFFSET
1,2
COMMENTS
This sequence is part of a solution of a more general problem involving two equations, three sequences a(n), b(n), c(n) and a constant A:
A * c(n)+1 = a(n)^2,
(A+1) * c(n)+1 = b(n)^2, for details see comment in A157014.
This sequence is the c(n) sequence for A=8.
LINKS
Colin Barker, Table of n, a(n) for n = 1..325
Index entries for linear recurrences with constant coefficients, signature (1155,-1155,1).
FORMULA
8*a(n)+1 = A077420(n-1)^2.
9*a(n)+1 = A046176(n)^2.
G.f.: 136*x^2/(-x^3+1155*x^2-1155*x+1).
a(1) = 0, a(2) = 136, a(3) = 1155*a(2), a(n) = 1155 * (a(n-1)-a(n-2)) + a(n-3) for n > 3.
a(n) = -((577+408*sqrt(2))^(-n)*(-1+(577+408*sqrt(2))^n)*(17+12*sqrt(2)+(-17+12*sqrt(2))*(577+408*sqrt(2))^n))/288. - Colin Barker, Jul 25 2016
Sum_{n>=2} 1/a(n) = 17/4 - 3*sqrt(2). - Amiram Eldar, Jan 29 2026
MATHEMATICA
LinearRecurrence[{1155, -1155, 1}, {0, 136, 157080}, 20] (* Harvey P. Dale, Dec 04 2019 *)
PROG
(PARI) concat(0, Vec(136*x^2/(-x^3+1155*x^2-1155*x+1) + O(x^20))) \\ Charles R Greathouse IV, Sep 26 2012
(PARI) a(n) = round(-((577+408*sqrt(2))^(-n)*(-1+(577+408*sqrt(2))^n)*(17+12*sqrt(2)+(-17+12*sqrt(2))*(577+408*sqrt(2))^n))/288) \\ Colin Barker, Jul 25 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Weisenhorn, Mar 08 2009
EXTENSIONS
Edited by Alois P. Heinz, Sep 09 2011
STATUS
approved