OFFSET
1,2
COMMENTS
Also values x of Pythagorean triples (x, x+127, y).
Corresponding values y of solutions (x, y) are in A159466.
For the generic case x^2+(x+p)^2 = y^2 with p = 2*m^2-1 a (prime) number in A066436 see A118673 or A129836.
Lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
Lim_{n -> infinity} a(n)/a(n-1) = (129+16*sqrt(2))/127 for n mod 3 = {1, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (34947+21922*sqrt(2))/127^2 for n mod 3 = 0.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
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) + 254 for n > 6; a(1)=0, a(2)=17, a(3)=308, a(4)=381, a(5)=468, a(6)=2117.
G.f.: x*(17+291*x+73*x^2-15*x^3-97*x^4-15*x^5) / ((1-x)*(1-6*x^3+x^6)).
a(3*k+1) = 127*A001652(k) for k >= 0.
MATHEMATICA
LinearRecurrence[{1, 0, 6, -6, 0, -1, 1}, {0, 17, 308, 381, 468, 2117, 2540}, 80] (* Vladimir Joseph Stephan Orlovsky, Feb 07 2012 *)
PROG
(PARI) {forstep(n=0, 500000000, [1, 3], if(issquare(2*n^2+254*n+16129), print1(n, ", ")))};
(Magma) I:=[0, 17, 308, 381, 468, 2117, 2540]; [n le 7 select I[n] else Self(n-1) + 6*Self(n-3) - 6*Self(n-4) - Self(n-6) + Self(n-7): n in [1..50]]; // G. C. Greubel, Mar 31 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Mohamed Bouhamida, Jun 14 2007
EXTENSIONS
Edited and two more terms added by Klaus Brockhaus, Apr 13 2009
STATUS
approved