OFFSET
1,2
COMMENTS
Corresponding values y of solutions (x, y) are in A161487.
lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
lim_{n -> infinity} a(n)/a(n-1) = (209+60*sqrt(2))/191 for n mod 3 = {1, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (52323+26522*sqrt(2))/191^2 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)+382 for n > 6; a(1)=0, a(2)=69, a(3)=336, a(4)=573, a(5)=936, a(6)=2449.
G.f.: x*(69+267*x+237*x^2-51*x^3-89*x^4-51*x^5) / ((1-x)*(1-6*x^3+x^6)).
a(3*k+1) = 191*A001652(k) for k >= 0.
MATHEMATICA
Transpose[NestList[Flatten[{Rest[#], 6#[[4]]-First[#]+382}]&, {0, 69, 336, 573, 936, 2449}, 40]][[1]] (* Harvey P. Dale, Apr 01 2011 *)
LinearRecurrence[{1, 0, 6, -6, 0, -1, 1}, {0, 69, 336, 573, 936, 2449, 3820}, 40] (* Harvey P. Dale, Mar 29 2016 *)
PROG
(PARI) {forstep(n=0, 10000000, [1, 3], if(issquare(2*n^2+382*n+36481), print1(n, ", ")))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Klaus Brockhaus, Jun 13 2009
STATUS
approved