%I #23 Sep 08 2022 08:45:48

%S 0,0,1,3,13,39,133,399,1261,3783,11605,34815,105469,316407,953317,

%T 2859951,8596237,25788711,77431669,232295007,697147165,2091441495,

%U 6275373061,18826119183,56482551853,169447655559,508359743893,1525079231679,4575304803901,13725914411703

%N a(n) = (4*3^n - 5*2^n + (-2)^n)/20.

%C a(n+1) - 3a(n) = 0,1,0,4,0,16,0,64,.. is an "aerated" version of A000302.

%H Vincenzo Librandi, <a href="/A167910/b167910.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 (3,4,-12).

%F a(2*n+1) = 3*a(2*n).

%F a(n) = 3*a(n-1) + 4*a(n-2) - 12*a(n-3).

%F G.f.: x^2/((1-3*x)*(1-2*x)*(1+2*x)). - _Philippe Deléham_, Nov 15 2009

%t LinearRecurrence[{3,4,-12},{0,0,1},40] (* _Harvey P. Dale_, Mar 29 2015 *)

%o (Magma) [(4*3^n-5*2^n+(-2)^n)/20: n in [0..40] ]; // _Vincenzo Librandi_, Aug 06 2011

%K nonn,easy

%O 0,4

%A _Paul Curtz_, Nov 15 2009

%E Replaced definition by Lava formula of Nov 26 2009. Removed comments about unrelated sequences. - _R. J. Mathar_, Feb 27 2010