OFFSET
1,2
COMMENTS
This sequence is part of a solution of a more general problem involving 2 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=7.
LINKS
Colin Barker, Table of n, a(n) for n = 1..300
Index entries for linear recurrences with constant coefficients, signature (899,-899,1).
FORMULA
7*a(n)+1 = A157877(n)^2.
8*a(n)+1 = A157878(n)^2.
G.f.: 120*x^2/(-x^3+899*x^2-899*x+1).
a(1) = 0, a(2) = 120, a(3) = 899*a(2), a(n) = 899 * (a(n-1)-a(n-2)) + a(n-3) for n > 3.
a(n) = -((449+120*sqrt(14))^(-n)*(-1+(449+120*sqrt(14))^n)*(15+4*sqrt(14)+(-15+4*sqrt(14))*(449+120*sqrt(14))^n))/224. - Colin Barker, Jul 25 2016
Sum_{n>=2} 1/a(n) = 15/4 - sqrt(14). - Amiram Eldar, Jan 29 2026
MATHEMATICA
CoefficientList[Series[120x^2/(-x^3+899x^2-899x+1), {x, 0, 30}], x] (* or *) LinearRecurrence[{899, -899, 1}, {0, 0, 120}, 30] (* Harvey P. Dale, Jan 14 2014 *)
PROG
(PARI) concat(0, Vec(120*x^2/(-x^3+899*x^2-899*x+1)+O(x^20))) \\ Charles R Greathouse IV, Sep 25 2012
(PARI) a(n) = round(-((449+120*sqrt(14))^(-n)*(-1+(449+120*sqrt(14))^n)*(15+4*sqrt(14)+(-15+4*sqrt(14))*(449+120*sqrt(14))^n))/224) \\ 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