OFFSET
1,1
COMMENTS
(-200, a(1)) and (A123654(n), a(n+1)) are solutions (x, y) to the Diophantine equation x^2+(x+809)^2 = y^2.
lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
lim_{n -> infinity} a(n)/a(n-1) = (873+232*sqrt(2))/809 for n mod 3 = {0, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (989043+524338*sqrt(2))/809^2 for n mod 3 = 1.
FORMULA
a(n) = 6*a(n-3)-a(n-6) for n > 6; a(1)=641, a(2)=809, a(3)=1105, a(4)=2741, a(5)=4045, a(6)=5989.
G.f.: (1-x)*(641+1450*x+2555*x^2+1450*x^3+641*x^4) / (1-6*x^3+x^6).
a(3*k-1) = 809*A001653(k) for k >= 1.
EXAMPLE
PROG
(PARI) {forstep(n=-200, 10000000, [3, 1], if(issquare(2*n^2+1618*n+654481, &k), print1(k, ", ")))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Klaus Brockhaus, May 18 2009
STATUS
approved