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%I #13 Sep 08 2022 08:45:29
%S 2,12,56,176,672,2496,9088,33536,123392,453632,1669120,6139904,
%T 22585344,83083264,305627136,1124270080,4135714816,15213527040,
%U 55964073984,205867974656,757300461568,2785785413632,10247716470784,37696978288640,138671105769472
%N a(n) = 2^n*tribonacci(n) or (2^n)*A001644(n+1).
%H G. C. Greubel, <a href="/A127214/b127214.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec_order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,4,8).
%F a(n) = Trace of matrix [({2,2,2},{2,0,0}m{0,2,0)^n].
%F a(n) = 2^n * Trace of matrix [({1,1,1},{1,0,0},0,1,0)^n].
%F From _Colin Barker_, Sep 02 2013: (Start)
%F a(n) = 2*a(n-1) + 4*a(n-2) + 8*a(n-3).
%F G.f.: -2*x*(12*x^2+4*x+1)/(8*x^3+4*x^2+2*x-1). (End)
%t Table[Tr[MatrixPower[2*{{1, 1, 1}, {1, 0, 0}, {0, 1, 0}}, x]], {x, 1, 20}]
%t LinearRecurrence[{2, 4, 8}, {2, 12, 56}, 50] (* _G. C. Greubel_, Dec 18 2017 *)
%o (PARI) x='x+O('x^30); Vec(-2*x*(12*x^2+4*x+1)/(8*x^3+4*x^2+2*x-1)) \\ _G. C. Greubel_, Dec 18 2017
%o (Magma) I:=[2,12,56]; [n le 3 select I[n] else 2*Self(n-1) + 4*Self(n-2) + 8*Self(n-3): n in [1..30]]; // _G. C. Greubel_, Dec 18 2017
%Y Cf. A087131, A127210, A127211, A127212, A127213, A127215, A127216.
%K nonn,easy
%O 1,1
%A _Artur Jasinski_, Jan 09 2007
%E More terms from _Colin Barker_, Sep 02 2013
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