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A131370 a(n) = 3a(n-1) - 3a(n-2) + 2a(n-3), a(0) = 3, a(1) = 2, a(2) = 0.

%I A131370 #20 Apr 28 2025 15:06:45
%S A131370 3,2,0,0,4,12,24,44,84,168,340,684,1368,2732,5460,10920,21844,43692,
%T A131370 87384,174764,349524,699048,1398100,2796204,5592408,11184812,22369620,
%U A131370 44739240,89478484,178956972,357913944,715827884,1431655764,2863311528
%N A131370 a(n) = 3a(n-1) - 3a(n-2) + 2a(n-3), a(0) = 3, a(1) = 2, a(2) = 0.
%C A131370 Sequence is identical to its third differences. Binomial transform of 3, -1, -1, 3, -1, -1, 3, -1, -1, ... .
%H A131370 Harvey P. Dale, <a href="/A131370/b131370.txt">Table of n, a(n) for n = 0..1000</a>
%H A131370 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3, -3, 2).
%F A131370 a(n) = 2^n/3 + (8/3)cos(n*Pi/3). - _Emeric Deutsch_, Oct 15 2007
%F A131370 G.f.: -(3-7*x+3*x^2)/(2*x-1)/(x^2-x+1). - _R. J. Mathar_, Nov 14 2007
%F A131370 a(n) = 2*A086953(n-1) for n>0. - _Rick L. Shepherd_, Aug 02 2017
%p A131370 seq((1/3)*2^n+8*cos((1/3)*n*Pi)*1/3,n=0..33); # _Emeric Deutsch_, Oct 15 2007
%t A131370 a = {3, 2, 0}; Do[AppendTo[a, 3*a[[ -1]] - 3*a[[ -2]] + 2*a[[ -3]]], {60}]; a (* _Stefan Steinerberger_, Oct 04 2007 *)
%t A131370 LinearRecurrence[{3,-3,2},{3,2,0},40] (* _Harvey P. Dale_, Apr 28 2025 *)
%Y A131370 Cf. A086953.
%K A131370 nonn,easy
%O A131370 0,1
%A A131370 _Paul Curtz_, Sep 30 2007
%E A131370 More terms from _Stefan Steinerberger_, Oct 04 2007