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

3, 27, 189, 891, 5103, 28431, 155277, 859491, 4743603, 26158707, 144374805, 796630059, 4395548511, 24254435799, 133832255589, 738466498755, 4074759563139, 22483948079115, 124063275771981, 684563868232731, 3777327684782127, 20842766314284447

Offset

1,1

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).

Formula

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

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

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

Mathematica

Table[Tr[MatrixPower[3*{{1, 1, 1}, {1, 0, 0}, {0, 1, 0}}, x]], {x, 1, 20}]
LinearRecurrence[{3, 9, 27}, {3, 27, 189}, 50] (* G. C. Greubel, Dec 18 2017 *)

Prog

(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
(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

Crossrefs

Cf. A087131, A127210, A127211, A127212, A127213, A127214, A127216.

Sequence in context: A370710 A241271 A222015 * A124813 A127220 A127222

Adjacent sequences: A127212 A127213 A127214 * A127216 A127217 A127218

Keyword

nonn,easy

Author

Artur Jasinski, Jan 09 2007

Extensions

More terms from Colin Barker, Sep 02 2013

Status

approved