OFFSET
1,2
COMMENTS
Also values x of Pythagorean triples (x, x+449, y).
Corresponding values y of solutions (x, y) are in A159589.
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) = (451+30*sqrt(2))/449 for n mod 3 = {1, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (507363+329222*sqrt(2))/449^2 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) +898 for n > 6; a(1)=0, a(2)=31, a(3)=1204, a(4)=1347, a(5)=1504, a(6)=8151.
G.f.: x*(31+1173*x+143*x^2-29*x^3-391*x^4-29*x^5)/((1-x)*(1-6*x^3+x^6)).
a(3*k+1) = 449*A001652(k) for k >= 0.
MATHEMATICA
LinearRecurrence[{1, 0, 6, -6, 0, -1, 1}, {0, 31, 1204, 1347, 1504, 8151, 8980}, 50] (* Vladimir Joseph Stephan Orlovsky, Feb 14 2012 *)
PROG
(PARI) {forstep(n=0, 500000000, [3, 1], if(issquare(2*n^2+898*n+201601), print1(n, ", ")))}
(PARI) x='x+O('x^30); concat([0], Vec(x*(31+1173*x+143*x^2-29*x^3-391*x^4 -29*x^5)/((1-x)*(1-6*x^3+x^6)))) \\ G. C. Greubel, May 08 2018
(Magma) I:=[0, 31, 1204, 1347, 1504, 8151, 8980]; [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 08 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mohamed Bouhamida, Jun 15 2007
EXTENSIONS
Edited and two terms added by Klaus Brockhaus, Apr 17 2009
STATUS
approved