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