%I #20 Sep 08 2022 08:45:17
%S 1,4,14,47,154,496,1577,4964,15502,48103,148490,456416,1397905,
%T 4268740,13002638,39522143,119912698,363262672,1099015481,3321204260,
%U 10026858766,30246156439,91171963754,274650794432,826923598369
%N a(n+3) = 6a(n+2) - 10a(n+1) + 3a(n); a(0) = 1, a(1) = 4, a(2) = 14.
%C Binomial transform of A104004.
%C If another a(0)=0 is added in front, also the binomial transform of A027934.
%H Harvey P. Dale, <a href="/A104487/b104487.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 (6,-10,3).
%F G.f.: (2*x-1)/((3*x-1)*(x^2-3*x+1)). Define c = (3+sqrt(5))/2 and d = (3-sqrt(5))/2. Then a(n) = 3^(n+1) - ((2*sqrt(5)/5)+1)*c^n + ((2*sqrt(5)/5)-1)*d^n = 3^(n+1) - Fibonacci(2n+3). - _Ralf Stephan_, May 20 2007
%t LinearRecurrence[{6,-10,3},{1,4,14},30] (* _Harvey P. Dale_, May 07 2017 *)
%o (Magma) [3^(n+1) - Fibonacci(2*n+3): n in [0..30]]; // _Vincenzo Librandi_, Apr 21 2011
%K nonn,easy
%O 0,2
%A _Creighton Dement_, Apr 19 2005
%E Comment concerning the binomial transforms corrected by _R. J. Mathar_, Oct 26 2009