OFFSET
1,1
COMMENTS
(-21,a(1)) and (A129991(n), a(n+1)) are solutions (x, y) to the Diophantine equation x^2+(x+241)^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)=221, a(2)=241, a(3)=265, a(4)=1061, a(5)=1205, a(6)=1369.
G.f.: x*(1-x)*(221+462*x+727*x^2+462*x^3+221*x^4) / (1-6*x^3+x^6).
a(3*k-1) = 241*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) = (243+22*sqrt(2))/241 for n mod 3 = {0, 2}.
Limit_{n -> oo} a(n)/a(n-1) = (137283+87958*sqrt(2))/241^2 for n mod 3 = 1.
EXAMPLE
MATHEMATICA
LinearRecurrence[{0, 0, 6, 0, 0, -1}, {221, 241, 265, 1061, 1205, 1369}, 30] (* Harvey P. Dale, Nov 21 2011 *)
PROG
(PARI) {forstep(n=-24, 50000000, [3, 1], if(issquare(2*n^2+482*n+58081, &k), print1(k, ", ")))}
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Klaus Brockhaus, Apr 16 2009
STATUS
approved