OFFSET
1,1
COMMENTS
The corresponding values of y are given by a(n+2).
Positive values of x (or y) satisfying x^2 - 18xy + y^2 + 704 = 0.
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,3,0,-1).
FORMULA
a(n) = 3*a(n-2)-a(n-4).
G.f.: -x*(x-1)*(3*x^2+7*x+3) / ((x^2-x-1)*(x^2+x-1)).
a(n) = F(n+2) + (-1)^n*F(n-3), n>1, with F the Fibonacci numbers (A000045). - Ralf Stephan, Feb 05 2014
Let h(n) = hypergeom([(1 - n)/2, n mod 2 - n/2], [1 - n], -4) then a(n) = h(n-1) + h(n) for n > 3. - Peter Luschny, Sep 03 2019
EXAMPLE
9 is in the sequence because (x, y) = (9, 23) is a solution to x^2 - 3xy + y^2 + 11 = 0.
PROG
(PARI) Vec(-x*(x-1)*(3*x^2+7*x+3)/((x^2-x-1)*(x^2+x-1)) + O(x^100))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Feb 04 2014
STATUS
approved