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a(n) = F(n^2)/F(n), where F(n) = A000045(n) is the n-th Fibonacci number.
5

%I #35 Feb 19 2024 01:58:02

%S 1,3,17,329,15005,1866294,598364773,505248088463,1114384187445409,

%T 6440451785077489365,97415813466381445596089,

%U 3858093084890921488916776332,400009475456580321242184872389193,108580324845164033411588204172311746011

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

%H Clark Kimberling, <a href="/A051294/b051294.txt">Table of n, a(n) for n = 1..69</a> (all terms with <= 1000 digits)

%F 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

%t Table[Fibonacci[n^2]/Fibonacci[n],{n,15}] (* _Harvey P. Dale_, Apr 12 2011 *)

%o (PARI) a(n)=fibonacci(n^2)/fibonacci(n)

%o (PARI) {Lucas(n)=fibonacci(n-1)+fibonacci(n+1)}

%o {a(n)=polcoeff(1/(1-Lucas(n)*x+(-1)^n*x^2+x*O(x^n)),n-1)} /* _Paul D. Hanna_, Jan 28 2012 */

%Y Main diagonal of array A028412.

%K easy,nonn

%O 1,2

%A _Leroy Quet_

%E More terms from _Benoit Cloitre_, Jan 05 2003