A014337 Three-fold exponential convolution of Fibonacci numbers with themselves (divided by 6).

0, 0, 0, 1, 6, 35, 180, 910, 4494, 22049, 107580, 523765, 2546280, 12370436, 60074196, 291677905, 1416019290, 6873991055, 33368325084, 161976597634, 786259649010, 3816607413905, 18526261416960

Offset

0,5

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,-1,-24,9).

Formula

a(n) = (1/30)(3^n*Fibonacci(n) - 3*Fibonacci(2n)). - Ralf Stephan, May 14 2004

G.f.: x^3/((1-3*x+x^2)*(1-3*x-9*x^2)). - Colin Barker, Mar 19 2012

Mathematica

CoefficientList[Series[x^3/((1-3*x+x^2)*(1-3*x-9*x^2)), {x, 0, 30}], x] (* Vincenzo Librandi, Mar 20 2012 *)

Prog

(PARI) a(n)=(3^n*fibonacci(n)-3*fibonacci(2*n))/30 \\ Charles R Greathouse IV, Mar 20 2012

Crossrefs

Cf. A014336.

Column k=3 of A346415.

Sequence in context: A030532 A333800 A026997 * A002041 A103995 A137628

Adjacent sequences: A014334 A014335 A014336 * A014338 A014339 A014340

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved