OFFSET
1,2
COMMENTS
Corresponding values y of solutions (x, y) are in A157120.
lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
lim_{n -> infinity} a(n)/a(n-1) = (11+3*sqrt(2))/(11-3*sqrt(2)) for n mod 3 = {1, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (3+2*sqrt(2))*(11-3*sqrt(2))^2/(11+3*sqrt(2))^2 for n mod 3 = 0.
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,0,6,-6,0,-1,1).
FORMULA
a(n) = 6*a(n-3)-a(n-6)+206 for n > 6; a(1) = 0, a(2) = 84, a(3) = 105, a(4) = 309, a(5) = 765, a(6) = 884.
G.f.: x*(84+21*x+204*x^2-48*x^3-7*x^4-48*x^5)/((1-x)*(1-6*x^3+x^6)).
a(3*k+1) = 103*A001652(k) for k >= 0.
PROG
(PARI) {forstep(n=0, 1300000000, [1, 3], if(issquare(2*n^2+206*n+10609), print1(n, ", ")))}
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Klaus Brockhaus, Feb 25 2009
STATUS
approved