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%I #17 Sep 08 2022 08:44:39
%S 0,0,0,6,36,210,1080,5460,26964,132294,645480,3142590,15277680,
%T 74222616,360445176,1750067430,8496115740,41243946330,200209950504,
%U 971859585804,4717557894060,22899644483430,111157568501760
%N Three-fold exponential convolution of Fibonacci numbers with themselves.
%H Nathaniel Johnston, <a href="/A014336/b014336.txt">Table of n, a(n) for n = 0..500</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,-1,-24,9).
%F (1/5)(3^n*Fibonacci(n) - 3*Fibonacci(2n)). - _Ralf Stephan_, May 14 2004
%F From _R. J. Mathar_, Jun 10 2013: (Start)
%F G.f.: -6*x^3 / ( (x^2-3*x+1)*(9*x^2+3*x-1) ).
%F a(n) = 6*A014337(n). (End)
%p with(combinat):A014336:=proc(n)return (1/5)*(3^n*fibonacci(n)-3*fibonacci(2*n)):end:
%p seq(A014336(n), n=0..22); # _Nathaniel Johnston_, Apr 18 2011
%o (Magma) [(1/5)*(3^n*Fibonacci(n) - 3*Fibonacci(2*n)): n in [0..30]]; // _Vincenzo Librandi_, Apr 18 2011
%Y Cf. A000045.
%K nonn,easy
%O 0,4
%A _N. J. A. Sloane_