OFFSET
1,1
COMMENTS
(-51, a(1)) and (A161486(n), a(n+1)) are solutions (x, y) to the Diophantine equation x^2+(x+191)^2 = y^2.
lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
lim_{n -> infinity} a(n)/a(n-1) = (209+60*sqrt(2))/191 for n mod 3 = {0, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (52323+26522*sqrt(2))/191^2 for n mod 3 = 1.
FORMULA
a(n) = 6*a(n-3)-a(n-6) for n > 6; a(1)=149, a(2)=191, a(3)=269, a(4)=625, a(5)=955, a(6)=1465.
G.f.: (1-x)*(149+340*x+609*x^2+340*x^3+149*x^4) / (1-6*x^3+x^6).
a(3*k-1) = 191*A001653(k) for k >= 1.
EXAMPLE
PROG
(PARI) {forstep(n=-52, 100000000, [1, 3], if(issquare(2*n^2+382*n+36481, &k), print1(k, ", ")))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Klaus Brockhaus, Jun 13 2009
STATUS
approved