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%I #25 Oct 03 2023 13:11:20
%S 0,3,12,66,309,1524,7356,35787,173568,842790,4090485,19856568,
%T 96384072,467861331,2271040644,11023873914,53510987541,259747827852,
%U 1260842371428,6120257564955,29708354037720,144207380197758
%N a(n) = Sum_{k=0..n} 3^k*F(k) where F(k) is the k-th Fibonacci number.
%H Seiichi Manyama, <a href="/A082987/b082987.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,6,-9).
%F a(0)=0, a(1)=3, a(2)=12, a(n)=4a(n-1)+6a(n-2)-9a(n-3).
%F G.f.: 3*x / ((x-1)*(9*x^2+3*x-1)). - _Colin Barker_, Jun 26 2013
%t LinearRecurrence[{4,6,-9},{0,3,12},30] (* _Harvey P. Dale_, Feb 03 2019 *)
%o (PARI) a(n)=if(n<0,0,sum(k=0,n,fibonacci(k)*3^k))
%Y Cf. A014334, A082988, A119282.
%K nonn,easy
%O 0,2
%A _Benoit Cloitre_, May 29 2003
%E Offset changed to 0 by _Seiichi Manyama_, Oct 03 2023
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