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A127213 a(n) = 6^n*Lucas(n), where Lucas = A000204. 10

%I

%S 6,108,864,9072,85536,839808,8118144,78941952,765904896,7437339648,

%T 72196614144,700923912192,6804621582336,66060990332928,

%U 641332318961664,6226189565755392,60445100877152256,586813429630107648

%N a(n) = 6^n*Lucas(n), where Lucas = A000204.

%H G. C. Greubel, <a href="/A127213/b127213.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,36).

%F a(n) = Trace of matrix [({6,6},{6,0})^n].

%F a(n) = 6^n * Trace of matrix [({1,1},{1,0})^n].

%F From _Colin Barker_, Sep 02 2013: (Start)

%F a(n) = 6*a(n-1) + 36*a(n-2).

%F G.f.: -6*x*(12*x+1)/(36*x^2+6*x-1). (End)

%t Table[6^n Tr[MatrixPower[{{1, 1}, {1, 0}}, x]], {x, 1, 20}]

%t Table[6^n*LucasL[n], {n,1,50}] (* _G. C. Greubel_, Dec 18 2017 *)

%o (PARI) x='x+O('x^30); Vec(-6*x*(12*x+1)/(36*x^2+6*x-1)) \\ _G. C. Greubel_, Dec 18 2017

%o (MAGMA) [6^n*Lucas(n): n in [1..30]]; // _G. C. Greubel_, Dec 18 2017

%Y Cf. A000204, A087131, A127210, A127211, A127212, A127214, A127215, A127216.

%K nonn,easy

%O 1,1

%A _Artur Jasinski_, Jan 09 2007

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Last modified August 8 23:02 EDT 2020. Contains 336300 sequences. (Running on oeis4.)