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A127215
a(n) = 3^n*tribonacci(n) or (3^n)*A001644(n+1).
6
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
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
KEYWORD
nonn,easy
AUTHOR
Artur Jasinski, Jan 09 2007
EXTENSIONS
More terms from Colin Barker, Sep 02 2013
STATUS
approved