OFFSET
1,2
COMMENTS
Also values x of Pythagorean triples (x, x+79, y).
Corresponding values y of solutions (x, y) are in A159758.
lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
lim_{n -> infinity} a(n)/a(n-1) = (83+18*sqrt(2))/79 for n mod 3 = {1, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (10659+6110*sqrt(2))/79^2 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) +158 for n > 6; a(1)=0, a(2)=20, a(3)=161, a(4)=237, a(5)=341, a(6)=1140.
G.f.: x*(20+141*x+76*x^2-16*x^3-47*x^4-16*x^5)/((1-x)*(1-6*x^3+x^6)).
a(3*k+1) = 79*A001652(k) for k >= 0.
MATHEMATICA
LinearRecurrence[{1, 0, 6, -6, 0, -1, 1}, {0, 20, 161, 237, 341, 1140, 1580}, 75] (* Vladimir Joseph Stephan Orlovsky, Feb 07 2012 *)
PROG
(PARI) forstep(n=0, 100000000, [1, 3], if(issquare(2*n^2+158*n+6241), print1(n, ", ")))
(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!(x*(20+141*x+76*x^2-16*x^3-47*x^4-16*x^5)/((1-x)*(1- 6*x^3+x^6)))); // G. C. Greubel, May 07 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mohamed Bouhamida, May 19 2006
EXTENSIONS
Edited by Klaus Brockhaus, Apr 30 2009
STATUS
approved