OFFSET
1,2
COMMENTS
Also values x of Pythagorean triples (x, x+47, y).
Corresponding values y of solutions (x, y) are in A159750.
lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
lim_{n -> infinity} a(n)/a(n-1) = (51+14*sqrt(2))/47 for n mod 3 = {1, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (3267+1702*sqrt(2))/47^2 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) +94 for n > 6; a(1)=0, a(2)=16, a(3)=85, a(4)=141, a(5)=225, a(6)=616.
G.f.: x*(16+69*x+56*x^2-12*x^3-23*x^4-12*x^5)/((1-x)*(1-6*x^3+x^6)).
a(3*k+1) = 47*A001652(k) for k >= 0.
MATHEMATICA
Select[Range[0, 100000], IntegerQ[Sqrt[#^2+(#+47)^2]]&] (* or *) LinearRecurrence[{1, 0, 6, -6, 0, -1, 1}, {0, 16, 85, 141, 225, 616, 940}, 50] (* Vladimir Joseph Stephan Orlovsky, Feb 02 2012 *)
PROG
(PARI) {forstep(n=0, 100000000, [1, 3], if(issquare(2*n^2+94+2209), print1(n, ", ")))}
(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!(x*(16+69*x+56*x^2-12*x^3-23*x^4-12*x^5)/((1-x)*(1-6*x^3 +x^6)))); // G. C. Greubel, May 07 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Mohamed Bouhamida, May 19 2006
EXTENSIONS
Edited by Klaus Brockhaus, Apr 30 2009
STATUS
approved