cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A014337 #29 Jul 08 2025 05:36:32
%S A014337 0,0,0,1,6,35,180,910,4494,22049,107580,523765,2546280,12370436,
%T A014337 60074196,291677905,1416019290,6873991055,33368325084,161976597634,
%U A014337 786259649010,3816607413905,18526261416960
%N A014337 Three-fold exponential convolution of Fibonacci numbers with themselves (divided by 6).
%H A014337 Vincenzo Librandi, <a href="/A014337/b014337.txt">Table of n, a(n) for n = 0..1000</a>
%H A014337 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,-1,-24,9).
%F A014337 a(n) = (1/30)(3^n*Fibonacci(n) - 3*Fibonacci(2n)). - _Ralf Stephan_, May 14 2004
%F A014337 G.f.: x^3/((1-3*x+x^2)*(1-3*x-9*x^2)). - _Colin Barker_, Mar 19 2012
%t A014337 CoefficientList[Series[x^3/((1-3*x+x^2)*(1-3*x-9*x^2)),{x,0,30}],x] (* _Vincenzo Librandi_, Mar 20 2012 *)
%o A014337 (PARI) a(n)=(3^n*fibonacci(n)-3*fibonacci(2*n))/30 \\ _Charles R Greathouse IV_, Mar 20 2012
%Y A014337 Cf. A014336.
%Y A014337 Column k=3 of A346415.
%K A014337 nonn,easy
%O A014337 0,5
%A A014337 _N. J. A. Sloane_