OFFSET
1,2
COMMENTS
Also values x of Pythagorean triples (x, x+577, y).
Corresponding values y of solutions (x, y) are in A159626.
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) = (579+34*sqrt(2))/577 for n mod 3 = {1, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (855171+556990*sqrt(2))/577^2 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)+1154 for n > 6; a(1)=0, a(2)=35, a(3)=1568, a(4)=1731, a(5)=1908, a(6)=10595.
G.f.: x*(35+1533*x+163*x^2-33*x^3-511*x^4-33*x^5) / ((1-x)*(1-6*x^3+x^6)).
a(3*k+1) = 577*A001652(k) for k >= 0.
MATHEMATICA
LinearRecurrence[{1, 0, 6, -6, 0, -1, 1}, {0, 35, 1568, 1731, 1908, 10595, 11540}, 30] (* Harvey P. Dale, May 27 2018 *)
PROG
(PARI) {forstep(n=0, 500000000, [3, 1], if(issquare(2*n^2+1154*n+332929), print1(n, ", ")))}
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mohamed Bouhamida, Jun 15 2007
EXTENSIONS
Edited and two terms added by Klaus Brockhaus, Apr 21 2009
STATUS
approved