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%I #21 Jan 02 2024 08:57:24
%S 1,3,9,11,33,99,313,939,2817,8435,25305,75915,227761,683283,2049849,
%T 6149531,18448593,55345779,166037353,498112059,1494336177,4483008515,
%U 13449025545,40347076635,121041229921,363123689763,1089371069289,3268113207851,9804339623553
%N a(n) = 3*a(n-1) - a(n-3) + 3*a(n-4) for n>3.
%H Colin Barker, <a href="/A135365/b135365.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,-1,3).
%F From _Richard Choulet_, Jan 02 2008: (Start)
%F a(n) = (1/7)*3^(n+1) + (4/3)*(-1)^n - (16/21)*cos(Pi*n/3) + (16*sqrt(3)/7)*sin(Pi*n/3).
%F a(n) = (1/7)*3^(n+1) + (1/7)*[4; 12; 36; -4; -12; -36] for n>=0. (End)
%F G.f.: (1 - 15*x^3) / ((1+x)*(1-3*x)*(1-x+x^2)). - _Colin Barker_, Feb 10 2016
%t Join[{1, 3}, LinearRecurrence[{3, 0, -1, 3}, {9, 11, 33, 99}, 25]] (* _G. C. Greubel_, Oct 11 2016 *)
%o (PARI) Vec((1-15*x^3)/((1+x)*(1-3*x)*(1-x+x^2)) + O(x^40)) \\ _Colin Barker_, Feb 10 2016
%Y Cf. A018282, A027894, A106305.
%K nonn,easy
%O 0,2
%A _Paul Curtz_, Dec 09 2007