OFFSET
1,2
COMMENTS
Also values x of Pythagorean triples (x, x+521, y).
Corresponding values y of solutions (x, y) are in A160583.
lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
lim_{n -> infinity} a(n)/a(n-1) = (537+92*sqrt(2))/521 for n mod 3 = {1, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (520659+314170*sqrt(2))/521^2 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)+1042 for n > 6; a(1)=0, a(2)=100, a(3)=1159, a(4)=1563, a(5)=2079, a(6)=8080.
G.f.: x*(100+1059*x+404*x^2-84*x^3-353*x^4-84*x^5) / ((1-x)*(1-6*x^3+x^6)).
a(3*k+1) = 521*A001652(k) for k >= 0.
MATHEMATICA
LinearRecurrence[{1, 0, 6, -6, 0, -1, 1}, {0, 100, 1159, 1563, 2079, 8080, 10420}, 50] (* Vladimir Joseph Stephan Orlovsky, Feb 13 2012 *)
PROG
(PARI) {forstep(n=0, 10000000, [3, 1], if(issquare(2*n^2+1042*n+271441), print1(n, ", ")))}
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mohamed Bouhamida, Jun 02 2007
EXTENSIONS
Edited and two terms added by Klaus Brockhaus, Jun 08 2009
STATUS
approved