A127220 a(n) = 3^n*tetranacci(n) or (2^n)*A001648(n).

3, 27, 189, 1215, 6318, 37179, 216513, 1253151, 7223661, 41806692, 241805655, 1398221271, 8084811933, 46753521975, 270362105694, 1563413859999, 9040715391141, 52279683047127, 302316992442837, 1748203962973380, 10109314209860523, 58458991419115875

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 (3,9,27,81).

Crossrefs

Cf. A087131, A127210, A127211, A127212, A127213, A127214, A127216, A001648, A127221, A127222.

Programs

Magma

I:=[3, 27, 189, 1215]; [n le 4 select I[n] else 3*Self(n-1) + 9*Self(n-2) + 27*Self(n-3) + 81*Self(n-4): n in [1..30]]; // G. C. Greubel, Dec 19 2017

Mathematica

Table[Tr[MatrixPower[3*{{1, 1, 1, 1}, {1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}}, x]], {x, 1, 20}]
LinearRecurrence[{3, 9, 27, 81}, {3, 27, 189, 1215}, 50] (* G. C. Greubel, Dec 19 2017 *)

PARI

x='x+O('x^30); Vec(-3*x*(108*x^3 +27*x^2 +6*x +1)/(81*x^4 +27*x^3 +9*x^2 +3*x -1)) \\ G. C. Greubel, Dec 19 2017

Formula

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

a(n) = 3^n * Trace of matrix [({1,1,1,1},{1,0,0,0},{0,1,0,0},{0,0,1,0})^n].

From Colin Barker, Sep 02 2013: (Start)

a(n) = 3*a(n-1) + 9*a(n-2) + 27*a(n-3) + 81*a(n-4).

G.f.: -3*x*(108*x^3+27*x^2+6*x+1)/(81*x^4+27*x^3+9*x^2+3*x-1). (End)

Extensions

More terms from Colin Barker, Sep 02 2013