OFFSET
1,2
COMMENTS
Also values x of Pythagorean triples (x, x+839, y).
Corresponding values y of solutions (x, y) are in A159896.
lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
lim_{n -> infinity} a(n)/a(n-1) = (843+58*sqrt(2))/839 for n mod 3 = {1, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (1760979+1141390*sqrt(2))/839^2 for n mod 3 = 0.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..3895
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) +1678 for n > 6; a(1)=0, a(2)=60, a(3)=2241, a(4)=2517, a(5)=2821, a(6)=15180.
G.f.: x*(60+2181*x+276*x^2-56*x^3-727*x^4-56*x^5)/((1-x)*(1-6*x^3+x^6)).
a(3*k+1) = 839*A001652(k) for k >= 0.
MATHEMATICA
LinearRecurrence[{1, 0, 6, -6, 0, -1, 1}, {0, 60, 2241, 2517, 2821, 15180, 16780}, 30] (* Harvey P. Dale, Jun 19 2014 *)
PROG
(PARI) {forstep(n=0, 100000000, [1, 3], if(issquare(2*n^2+1678*n+703921), print1(n, ", ")))}
(Magma) I:=[0, 60, 2241, 2517, 2821, 15180, 16780]; [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..30]]; // G. C. Greubel, May 17 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mohamed Bouhamida, Jun 20 2007
EXTENSIONS
Edited and two terms added by Klaus Brockhaus, Apr 30 2009
STATUS
approved