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

6, 108, 864, 9072, 85536, 839808, 8118144, 78941952, 765904896, 7437339648, 72196614144, 700923912192, 6804621582336, 66060990332928, 641332318961664, 6226189565755392, 60445100877152256, 586813429630107648

Offset: 1

Author

Artur Jasinski, Jan 09 2007

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (6,36).

Crossrefs

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

Programs

Magma

[6^n*Lucas(n): n in [1..30]]; // G. C. Greubel, Dec 18 2017

Mathematica

Table[6^n Tr[MatrixPower[{{1, 1}, {1, 0}}, x]], {x, 1, 20}]
Table[6^n*LucasL[n], {n,1,50}] (* G. C. Greubel, Dec 18 2017 *)
LinearRecurrence[{6,36},{6,108},20] (* Harvey P. Dale, Jan 20 2024 *)

PARI

x='x+O('x^30); Vec(-6*x*(12*x+1)/(36*x^2+6*x-1)) \\ G. C. Greubel, Dec 18 2017

Formula

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

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

From Colin Barker, Sep 02 2013: (Start)

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

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