A051294 a(n) = F(n^2)/F(n), where F(n) = A000045(n) is the n-th Fibonacci number.

1, 3, 17, 329, 15005, 1866294, 598364773, 505248088463, 1114384187445409, 6440451785077489365, 97415813466381445596089, 3858093084890921488916776332, 400009475456580321242184872389193, 108580324845164033411588204172311746011, 77162132055850720265395402022419687035969985

Offset

1,2

Links

Clark Kimberling, Table of n, a(n) for n = 1..69 (all terms with <= 1000 digits)

Formula

a(n) = [x^(n-1)] 1/(1 - Lucas(n)*x + (-1)^n*x^2), where Lucas(n) = A000204(n). - Paul D. Hanna, Jan 28 2012

Maple

a:= n-> (f->f(n^2)/f(n))(k->(<<0|1>, <1|1>>^k)[1, 2]):
seq(a(n), n=1..15);  # Alois P. Heinz, May 08 2025

Mathematica

Table[Fibonacci[n^2]/Fibonacci[n], {n, 15}]  (* Harvey P. Dale, Apr 12 2011 *)

Prog

(PARI) a(n)=fibonacci(n^2)/fibonacci(n)
(PARI) {Lucas(n)=fibonacci(n-1)+fibonacci(n+1)}
{a(n)=polcoeff(1/(1-Lucas(n)*x+(-1)^n*x^2+x*O(x^n)), n-1)} /* Paul D. Hanna, Jan 28 2012 */

Crossrefs

Main diagonal of array A028412.

Sequence in context: A271609 A290806 A009592 * A192556 A144033 A349643

Adjacent sequences: A051291 A051292 A051293 * A051295 A051296 A051297

Keyword

nonn,easy

Author

Leroy Quet

Extensions

More terms from Benoit Cloitre, Jan 05 2003

Status

approved