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A127215 a(n) = 3^n*tribonacci(n) or (3^n)*A001644(n+1). 6

%I

%S 3,27,189,891,5103,28431,155277,859491,4743603,26158707,144374805,

%T 796630059,4395548511,24254435799,133832255589,738466498755,

%U 4074759563139,22483948079115,124063275771981,684563868232731,3777327684782127,20842766314284447

%N a(n) = 3^n*tribonacci(n) or (3^n)*A001644(n+1).

%H G. C. Greubel, <a href="/A127215/b127215.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 (3,9,27).

%F a(n) = Trace of matrix [({3,3,3},{3,0,0},{0,3,0)^n].

%F a(n) = 3^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) = 3*a(n-1) + 9*a(n-2) + 27*a(n-3).

%F G.f.: -3*x*(27*x^2+6*x+1)/(27*x^3+9*x^2+3*x-1). (End)

%t Table[Tr[MatrixPower[3*{{1, 1, 1}, {1, 0, 0}, {0, 1, 0}}, x]], {x, 1, 20}]

%t LinearRecurrence[{3, 9, 27}, {3, 27, 189}, 50] (* _G. C. Greubel_, Dec 18 2017 *)

%o (PARI) x='x+O('x^30); Vec(-3*x*(27*x^2+6*x+1)/(27*x^3+9*x^2+3*x-1)) \\ _G. C. Greubel_, Dec 18 2017

%o (MAGMA) I:=[3,27,189]; [n le 3 select I[n] else 3*Self(n-1) + 9*Self(n-2) + 27*Self(n-3): n in [1..30]]; // _G. C. Greubel_, Dec 18 2017

%Y Cf. A087131, A127210, A127211, A127212, A127213, A127214, 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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Last modified September 27 16:11 EDT 2020. Contains 337383 sequences. (Running on oeis4.)