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%I #14 Sep 08 2022 08:45:29
%S 2,12,56,240,832,3264,12672,48896,187904,724992,2795520,10776576,
%T 41541632,160153600,617414656,2380201984,9175957504,35374497792,
%U 136373075968,525735034880,2026773676032,7813464064000,30121872326656,116123550875648,447670682386432
%N a(n) = 2^n*tetranacci(n) or (2^n)*A001648(n).
%H Indranil Ghosh, <a href="/A127216/b127216.txt">Table of n, a(n) for n = 1..1702</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,4,8,16).
%F a(n) = Trace of matrix [({{2,2,2,2},{2,0,0,0},{0,2,0,0),{0,0,2,0}})^n] a(n) = 2^n Trace of matrix [({{1,1,1,1},{1,0,0,0},{0,1,0,0},{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) + 16*a(n-4).
%F G.f.: -2*x*(32*x^3+12*x^2+4*x+1) / (16*x^4+8*x^3+4*x^2+2*x-1). (End)
%e a(8) = (2^8) * A001648(8) = 256 * 191 = 48896. - _Indranil Ghosh_, Feb 09 2017
%t Table[Tr[MatrixPower[2*{{1, 1, 1, 1}, {1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}}, x]], {x, 1, 20}]
%t LinearRecurrence[{2, 4, 8, 16}, {2, 12, 56, 240}, 50] (* _G. C. Greubel_, Dec 19 2017 *)
%o (PARI) x='x+O('x^30); Vec(-2*x*(32*x^3+12*x^2+4*x+1)/(16*x^4 +8*x^3 +4*x^2 +2*x -1)) \\ _G. C. Greubel_, Dec 19 2017
%o (Magma) I:=[2,12,56,240]; [n le 4 select I[n] else 2*Self(n-1) + 4*Self(n-2) + 8*Self(n-3) + 16*Self(n-4): n in [1..30]]; // _G. C. Greubel_, Dec 19 2017
%Y Cf. A087131, A127210, A127211, A127212, A127213, A127214, A127216, A001648.
%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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