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%I #15 Aug 02 2017 12:03:13
%S 3,2,0,0,4,12,24,44,84,168,340,684,1368,2732,5460,10920,21844,43692,
%T 87384,174764,349524,699048,1398100,2796204,5592408,11184812,22369620,
%U 44739240,89478484,178956972,357913944,715827884,1431655764,2863311528
%N a(n) = 3a(n-1) - 3a(n-2) + 2a(n-3), a(0) = 3, a(1) = 2, a(2) = 0.
%C Sequence is identical to its third differences. Binomial transform of 3, -1, -1, 3, -1, -1, 3, -1, -1, ... .
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3, -3, 2).
%F a(n) = 2^n/3 + (8/3)cos(n*Pi/3). - _Emeric Deutsch_, Oct 15 2007
%F G.f.: -(3-7*x+3*x^2)/(2*x-1)/(x^2-x+1). - _R. J. Mathar_, Nov 14 2007
%F a(n) = 2*A086953(n-1) for n>0. - _Rick L. Shepherd_, Aug 02 2017
%p seq((1/3)*2^n+8*cos((1/3)*n*Pi)*1/3,n=0..33); # _Emeric Deutsch_, Oct 15 2007
%t a = {3, 2, 0}; Do[AppendTo[a, 3*a[[ -1]] - 3*a[[ -2]] + 2*a[[ -3]]], {60}]; a (* _Stefan Steinerberger_, Oct 04 2007 *)
%Y Cf. A086953.
%K nonn,easy
%O 0,1
%A _Paul Curtz_, Sep 30 2007
%E More terms from _Stefan Steinerberger_, Oct 04 2007
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