OFFSET
1,2
COMMENTS
Also values x of Pythagorean triples (x, x+137, y).
Corresponding values y of solutions (x, y) are in A157213.
lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
lim_{n -> infinity} a(n)/a(n-1) = (18+5*sqrt(2))/(18-5*sqrt(2)) for n mod 3 = {1, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (3+2*sqrt(2))*(18-5*sqrt(2))^2/(18+5*sqrt(2))^2 for n mod 3 = 0.
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,0,6,-6,0,-1,1).
FORMULA
a(n) = 6*a(n-3)-a(n-6)+274 for n > 6; a(1)=0, a(2)=115, a(3)=136, a(4)=411, a(5)=1036, a(6)=1155.
G.f.: x*(115+21*x+275*x^2-65*x^3-7*x^4-65*x^5)/((1-x)*(1-6*x^3+x^6)).
a(3*k+1) = 137*A001652(k) for k >= 0.
MATHEMATICA
LinearRecurrence[{1, 0, 6, -6, 0, -1, 1}, {0, 115, 136, 411, 1036, 1155, 2740}, 80] (* Vladimir Joseph Stephan Orlovsky, Feb 07 2012 *)
PROG
(PARI) {forstep(n=0, 1500000000, [3, 1], if(issquare(2*n^2+274*n+18769), print1(n, ", ")))}
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mohamed Bouhamida, May 30 2007
EXTENSIONS
Edited and extended by Klaus Brockhaus, Feb 25 2009
STATUS
approved