A014336 Three-fold exponential convolution of Fibonacci numbers with themselves.

0, 0, 0, 6, 36, 210, 1080, 5460, 26964, 132294, 645480, 3142590, 15277680, 74222616, 360445176, 1750067430, 8496115740, 41243946330, 200209950504, 971859585804, 4717557894060, 22899644483430, 111157568501760

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Nathaniel Johnston, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (6,-1,-24,9).

Crossrefs

Cf. A000045.

Programs

Magma

[(1/5)*(3^n*Fibonacci(n) - 3*Fibonacci(2*n)): n in [0..30]]; // Vincenzo Librandi, Apr 18 2011

Maple

with(combinat):A014336:=proc(n)return (1/5)*(3^n*fibonacci(n)-3*fibonacci(2*n)):end:
seq(A014336(n), n=0..22); # Nathaniel Johnston, Apr 18 2011

Formula

(1/5)(3^n*Fibonacci(n) - 3*Fibonacci(2n)). - Ralf Stephan, May 14 2004

From R. J. Mathar, Jun 10 2013: (Start)

G.f.: -6*x^3 / ( (x^2-3*x+1)*(9*x^2+3*x-1) ).

a(n) = 6*A014337(n). (End)