OFFSET
1,2
COMMENTS
Also values x of Pythagorean triples (x, x+967, y).
Corresponding values y of solutions (x, y) are in A159701.
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) = (969+44**sqrt(2))/967 for n mod 3 = {1, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (2487411+1629850*sqrt(2))/967^2 for n mod 3 = 0.
LINKS
Harvey P. Dale, 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)+1934 for n > 6; a(1)=0, a(2)=45, a(3)=2688, a(4)=2901, a(5)=3128, a(6)=18105.
G.f.: x*(45+2643*x+213*x^2-43*x^3-881*x^4-43*x^5) / ((1-x)*(1-6*x^3+x^6)).
a(3*k+1) = 967*A001652(k) for k >= 0.
a(1)=0, a(2)=45, a(3)=2688, a(4)=2901, a(5)=3128, a(6)=18105, a(7)=19340, a(n)=a(n-1)+6*a(n-3)-6*a(n-4)-a(n-6)+a(n-7). - Harvey P. Dale, Nov 03 2013
MATHEMATICA
LinearRecurrence[{1, 0, 6, -6, 0, -1, 1}, {0, 45, 2688, 2901, 3128, 18105, 19340}, 40] (* Harvey P. Dale, Nov 03 2013 *)
PROG
(PARI) {forstep(n=0, 10000000, [1, 3], if(issquare(2*n^2+1934*n+935089), print1(n, ", ")))}
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mohamed Bouhamida, Jun 15 2007
EXTENSIONS
Edited and two terms added by Klaus Brockhaus, Apr 21 2009
STATUS
approved