A014336 - OEIS

%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_