A215044 a(n) = F(2*n)^5 with F=A000045 (Fibonacci numbers).
0, 1, 243, 32768, 4084101, 503284375, 61917364224, 7615646045657, 936668172433707, 115202670521319424, 14168993617568728125, 1742671044798615789551, 214334370099947863277568, 26361384861716322814590193
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (144,-2640,6930,-2640,144,-1).
Programs
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Magma
[Fibonacci(2*n)^5: n in [0..15]]; // Vincenzo Librandi, Sep 02 2012
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Mathematica
Table[Fibonacci[2*n]^5, {n,0,15}] (* Vincenzo Librandi, Sep 02 2012 *) -
PARI
a(n)=fibonacci(2*n)^5 \\ Charles R Greathouse IV, Oct 16 2015
Formula
O.g.f.: x*(1 + 99*x + 416*x^2 + 99*x^3 + x^4)/((1-3*x+x^2)*(1-18*x+x^2)*(1-123*x+x^2)), (from the even part of the bisection of A056572).
a(n) = (5*F(4*n) - 4*F(8*n) + F(12*n))/(5^2*L(2*n)), with L=A000032 (Lucas). See the third row in the signed triangle A039598, called in a general comment S.
a(n) = (10*F(2*n) - 5*F(6*n) + F(10*n))/5^2, from the partial fraction decomposition of the o.g.f. - Wolfdieter Lang, Oct 11 2012