OFFSET
1,1
COMMENTS
(-60, a(1)) and (A129626(n), a(n+1)) are solutions (x, y) to the Diophantine equation x^2+(x+281)^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)=229, a(2)=281, a(3)=365, a(4)=1009, a(5)=1405, a(6)=1961.
G.f.: x*(1-x)*(229+510*x+875*x^2+510*x^3+229*x^4) / (1-6*x^3+x^6).
a(3*k-1) = 281*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) = (297+68*sqrt(2))/281 for n mod 3 = {0, 2}.
Limit_{n -> oo} a(n)/a(n-1) = (130803+73738*sqrt(2))/281^2 for n mod 3 = 1.
EXAMPLE
PROG
(PARI) {forstep(n=-60, 200000000, [3, 1], if(issquare(2*n^2+562*n+78961, &k), print1(k, ", ")))}
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Klaus Brockhaus, Apr 12 2009
STATUS
approved