login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

a(n) = F(2*n+1)^5 with n >= 0, F=A000045 (Fibonacci numbers).
2

%I #23 Oct 01 2024 15:35:48

%S 1,32,3125,371293,45435424,5584059449,686719856393,84459630100000,

%T 10387823949447757,1277617458486664901,157136551895768914976,

%U 19326518128014212635057,2377004590722802744140625,292352238096435536675521568

%N a(n) = F(2*n+1)^5 with n >= 0, F=A000045 (Fibonacci numbers).

%H Vincenzo Librandi, <a href="/A215045/b215045.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (144,-2640,6930,-2640,144,-1).

%F O.g.f.: (1-x)*(1-111*x+1046*x^2-111*x^3+x^4)/((1-3*x+x^2)*(1-18*x+x^2)*(1-123*x+x^2)). From the odd part of the bisection of A056572.

%t Table[Fibonacci[2*n+1]^5, {n,0,201}] (* _Vincenzo Librandi_, Sep 02 2012 *)

%t Fibonacci[Range[1,35,2]]^5 (* _Harvey P. Dale_, Apr 05 2019 *)

%o (Magma) [Fibonacci(2*n+1)^5: n in [0..15]]; // _Vincenzo Librandi_, Sep 02 2012

%Y Cf. A000045, A056572, A215044 (even part).

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Aug 31 2012