This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A127214 #19 Sep 19 2024 21:58:55
%S A127214 2,12,56,176,672,2496,9088,33536,123392,453632,1669120,6139904,
%T A127214 22585344,83083264,305627136,1124270080,4135714816,15213527040,
%U A127214 55964073984,205867974656,757300461568,2785785413632,10247716470784,37696978288640,138671105769472
%N A127214 a(n) = 2^n*tribonacci(n) or (2^n)*A001644(n+1).
%H A127214 G. C. Greubel, <a href="/A127214/b127214.txt">Table of n, a(n) for n = 1..1000</a>
%H A127214 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,4,8).
%F A127214 a(n) = Trace of matrix [({2,2,2},{2,0,0},{0,2,0})^n].
%F A127214 a(n) = 2^n * Trace of matrix [({1,1,1},{1,0,0},{0,1,0})^n].
%F A127214 From _Colin Barker_, Sep 02 2013: (Start)
%F A127214 a(n) = 2*a(n-1) + 4*a(n-2) + 8*a(n-3).
%F A127214 G.f.: -2*x*(12*x^2+4*x+1)/(8*x^3+4*x^2+2*x-1). (End)
%t A127214 Table[Tr[MatrixPower[2*{{1, 1, 1}, {1, 0, 0}, {0, 1, 0}}, x]], {x, 1, 20}]
%t A127214 LinearRecurrence[{2, 4, 8}, {2, 12, 56}, 50] (* _G. C. Greubel_, Dec 18 2017 *)
%o A127214 (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 A127214 (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 A127214 Cf. A087131, A127210, A127211, A127212, A127213, A127215, A127216.
%K A127214 nonn,easy
%O A127214 1,1
%A A127214 _Artur Jasinski_, Jan 09 2007
%E A127214 More terms from _Colin Barker_, Sep 02 2013