1,1

Square roots of k^2+(k+17)^2 are in A156567, values k are in A118337.

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

lim_{n -> infinity} a(n)/a(n-1) = ((627+238*sqrt(2))/23^2)^2 for n mod 3 = 1.

lim_{n -> infinity} a(n)/a(n-1) = ((27+10*sqrt(2))/23)^2 for n mod 3 = {0, 2}.

a(n) = 34*a(n-3)-a(n-6)-4232 for n > 6; a(1)=289, a(2)=529, a(3)=1369, a(4)=4225, a(5)=13225, a(6)=42025.

G.f.: x*(289+240*x+840*x^2-6970*x^3+840*x^4+240*x^5+289*x^6)/((1-x)*(1-34*x^3+x^6)).

4225 = 65^2 is of the form k^2+(k+23)^2 with k = 33: 33^2+56^2 = 4225. Hence 4225 is in the sequence.

(PARI) {forstep(n=-8, 1800000, [1, 3], if(issquare(a=2*n*(n+23)+529), print1(a, ", ")))}

Equals A156567^2. Cf. A156575 (first trisection), A156573 (second trisection), A156574 (third trisection).

Cf. A118337, A156035 (decimal expansion of 3+2*sqrt(2)), A156164 (decimal expansion of 17+12*sqrt(2)), A156571 (decimal expansion of (27+10*sqrt(2))/23), A157472 (decimal expansion of (627+238*sqrt(2))/23^2).

Sequence in context: A107739 A008367 A152852 this_sequence A157990 A112077 A152934

Adjacent sequences: A156569 A156570 A156571 this_sequence A156573 A156574 A156575

nonn

Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Feb 11 2009

Revised by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Feb 16 2009

G.f. corrected, third comment and cross-references edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Sep 22 2009