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%I #21 Sep 08 2022 08:45:03
%S 3,3,9,21,57,153,423,1179,3321,9415,26843,76869,220951,637107,1842129,
%T 5339133,15507641,45127965,131548859,384059009,1122835671,3286907517,
%U 9633053985,28262033613,82998088607,243963263943,717698981853,2112976735749
%N a(0)=3; thereafter, a(n) = A002426(n+1) + Fibonacci(n-1)*(Fibonacci(n-1) + 1).
%H G. C. Greubel, <a href="/A059728/b059728.txt">Table of n, a(n) for n = 0..1000</a>
%H G. E. Andrews, <a href="http://www.mat.univie.ac.at/~slc/opapers/s25andrews.html">Three aspects of partitions</a>, Séminaire Lotharingien de Combinatoire, B25f (1990), 1 p.
%H L. Euler, <a href="http://eulerarchive.maa.org/pages/E326.html">(E326) Observationes analyticae</a>, also reprinted in: Opera Omnia. Teubner, Leipzig, 1911, Series (1), Vol. 15, p. 54.
%e a(6) = F_5*(F_5+1) + A002426(7) = 30 + 393 = 423.
%t b[n_] := If[n < 0, 0, 3^n Hypergeometric2F1[1/2, -n, 1, 4/3]]; Table[b[n + 1] + Fibonacci[n - 1]*(1 + Fibonacci[n - 1]), {n, 0,50}] (* _G. C. Greubel_, Feb 27 2017 *)
%o (Magma) P<x>:=PolynomialRing(Integers()); [Max(Coefficients((1+x+x^2)^(n+1)))+(Fibonacci(n-1)*(Fibonacci(n-1)+1)): n in [0..30]]; // _Vincenzo Librandi_, Dec 24 2016
%K nonn
%O 0,1
%A _N. J. A. Sloane_, Feb 09 2001
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