1,1

Square roots of k^2+(k+17)^2 are in A155923, values k (except for -5) are in A118120.

lim_{n -> infinity} a(n)/a(n-3) = (17+12*sqrt(2)).

lim_{n -> infinity} a(n)/a(n-1) = ((19+6*sqrt(2))/17)^2 for n mod 3 = {0, 2}.

lim_{n -> infinity} a(n)/a(n-1) = ((387+182*sqrt(2))/17^2)^2 for n mod 3 = 1.

a(n) = 34*a(n-3)-a(n-6)-2312 for n > 6; a(1)=169, a(2)=289, a(3)=625, a(4)=2809, a(5)=7225, a(6)=18769.

G.f.: x*(169+120*x+336*x^2-3562*x^3+336*x^4+120*x^5+169*x^6)/((1-x)*(1-34*x^3+x^6)).

625 = 25^2 is of the form k^2+(k+17)^2 with k = 7: 7^2+24^2 = 625. Hence 625 is in the sequence.

(PARI) {forstep(n=-5, 1600000, [1, 3], if(issquare(a=2*n*(n+17)+289), print1(a, ", ")))}

Equals A155923^2. Cf. A156160 (first trisection), A156161 (second trisection), A156162 (third trisection).

Cf. A118120, A156035 (decimal expansion of 3+2*sqrt(2)), A156164 (decimal expansion of 17+12*sqrt(2)), A156163 (decimal expansion of (19+6*sqrt(2))/17), A157649 (decimal expansion of (387+182*sqrt(2))/17^2).

Sequence in context: A124979 A018820 A020249 this_sequence A099011 A112076 A069645

Adjacent sequences: A156156 A156157 A156158 this_sequence A156160 A156161 A156162

nonn

Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Feb 09 2009

G.f. corrected, fourth comment and cross-references edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Sep 23 2009