OFFSET
1,2
COMMENTS
Also values x of Pythagorean triples (x, x+199, y).
Corresponding values y of solutions (x, y) are in A159548.
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) = (201+20*sqrt(2))/199 for n mod 3 = {1, 2}.
Lim_{n -> infinity} a(n)/a(n-1) = (91443+58282*sqrt(2))/199^2 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) + 398 for n > 6; a(1)=0, a(2)=21, a(3)=504, a(4)=597, a(5)=704, a(6)=3441.
G.f.: x*(21+483*x+93*x^2-19*x^3-161*x^4-19*x^5) / ((1-x)*(1-6*x^3+x^6)).
a(3*k+1) = 199*A001652(k) for k >= 0.
a(1)=0, a(2)=21, a(3)=504, a(4)=597, a(5)=704, a(6)=3441, a(7)=3980, a(n)=a(n-1)+6*a(n-3)-6*a(n-4)-a(n-6)+a(n-7). - Harvey P. Dale, Jun 03 2012
MATHEMATICA
LinearRecurrence[{1, 0, 6, -6, 0, -1, 1}, {0, 21, 504, 597, 704, 3441, 3980}, 30] (* Harvey P. Dale, Jun 03 2012 *)
PROG
(PARI) {forstep(n=0, 500000000, [1, 3], if(issquare(2*n^2+398*n+39601), print1(n, ", ")))};
(MAGMA) I:=[0, 21, 504, 597, 704, 3441, 3980]; [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..50]]; // G. C. Greubel, Mar 31 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Jun 14 2007
EXTENSIONS
Edited and two terms added by Klaus Brockhaus, Apr 14 2009
STATUS
approved