OFFSET
1,1
COMMENTS
(-341, a(1)) and (A122694(n), a(n+1)) are solutions (x, y) to the Diophantine equation x^2+(x+761)^2 = y^2.
lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
lim_{n -> infinity} a(n)/a(n-1) = (1003+462*sqrt(2))/761 for n mod 3 = {0, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (591603+85478*sqrt(2))/761^2 for n mod 3 = 1.
FORMULA
a(n) = 6*a(n-3)-a(n-6) for n > 6; a(1)=541, a(2)=761, a(3)=1465, a(4)=1781, a(5)=3805, a(6)=8249.
G.f.: (1-x)*(541+1302*x+2767*x^2+1302*x^3+541*x^4) / (1-6*x^3+x^6).
a(3*k-1) = 761*A001653(k) for k >= 1.
EXAMPLE
PROG
(PARI) {forstep(n=-344, 10000000, [3, 1], if(issquare(2*n^2+1522*n+579121, &k), print1(k, ", ")))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Klaus Brockhaus, May 18 2009
STATUS
approved