OFFSET
1,1
COMMENTS
(-35,a(1)) and (A130013(n), a(n+1)) are solutions (x, y) to the Diophantine equation x^2+(x+647)^2 = y^2.
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,6,0,0,-1).
FORMULA
a(n) = 6*a(n-3)-a(n-6) for n > 6; a(1)=613, a(2)=647, a(3)=685, a(4)=2993, a(5)=3235, a(6)=3497.
G.f.: (1-x)*(613+1260*x+1945*x^2+1260*x^3+613*x^4) / (1-6*x^3+x^6).
a(3*k-1) = 647*A001653(k) for k >= 1.
Limit_{n -> oo} a(n)/a(n-3) = 3+2*sqrt(2).
Limit_{n -> oo} a(n)/a(n-1) = (649+36*sqrt(2))/647 for n mod 3 = {0, 2}.
Limit_{n -> oo} a(n)/a(n-1) = (1084467+707402*sqrt(2))/647^2 for n mod 3 = 1.
EXAMPLE
MATHEMATICA
LinearRecurrence[{0, 0, 6, 0, 0, -1}, {613, 647, 685, 2993, 3235, 3497}, 30] (* Harvey P. Dale, Jun 22 2022 *)
PROG
(PARI) {forstep(n=-36, 10000000, [1, 3], if(issquare(2*n^2+1294*n+418609, &k), print1(k, ", ")))}
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Klaus Brockhaus, Apr 21 2009
STATUS
approved