A059728 a(0)=3; thereafter, a(n) = A002426(n+1) + Fibonacci(n-1)*(Fibonacci(n-1) + 1).

3, 3, 9, 21, 57, 153, 423, 1179, 3321, 9415, 26843, 76869, 220951, 637107, 1842129, 5339133, 15507641, 45127965, 131548859, 384059009, 1122835671, 3286907517, 9633053985, 28262033613, 82998088607, 243963263943, 717698981853, 2112976735749

Offset: 0

Author

N. J. A. Sloane, Feb 09 2001

Keywords

• nonn

Examples

			a(6) = F_5*(F_5+1) + A002426(7) = 30 + 393 = 423.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• G. E. Andrews, Three aspects of partitions, Séminaire Lotharingien de Combinatoire, B25f (1990), 1 p.
• L. Euler, (E326) Observationes analyticae, also reprinted in: Opera Omnia. Teubner, Leipzig, 1911, Series (1), Vol. 15, p. 54.

Programs

Magma

P:=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

Mathematica

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 *)