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, 539571113341926, 2619135664994016, 12713558032930800

Offset

0,4

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).

Formula

a(n) = (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)

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

Mathematica

A014336[n_] := (3^n*Fibonacci[n] - 3*Fibonacci[2*n])/5; Array[A014336, 30, 0] (* Paolo Xausa, Jun 05 2026 *)
(* Alternative: *)
LinearRecurrence[{6, -1, -24, 9}, {0, 0, 0, 6}, 30] (* Paolo Xausa, Jun 05 2026 *)

Prog

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

Crossrefs

Cf. A000045, A014337.

Sequence in context: A064238 A354229 A354231 * A268941 A269637 A269534

Adjacent sequences: A014333 A014334 A014335 * A014337 A014338 A014339

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved