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A014337
Three-fold exponential convolution of Fibonacci numbers with themselves (divided by 6).
3
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
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved