A033139 Base 3 digits are, in order, the first n terms of the periodic sequence with initial period 1,0,0.

1, 3, 9, 28, 84, 252, 757, 2271, 6813, 20440, 61320, 183960, 551881, 1655643, 4966929, 14900788, 44702364, 134107092, 402321277, 1206963831, 3620891493, 10862674480, 32588023440, 97764070320, 293292210961, 879876632883

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (3,0,1,-3).

Crossrefs

Cf. A000975.

Programs

Mathematica

CoefficientList[Series[1/((1-3x)(1-x^3)),{x,0,1001}],x] (* Vincenzo Librandi, Apr 04 2012 *)

PARI

x='x+O('x^50); Vec(1/((1-3*x)*(1-x^3))) \\ G. C. Greubel, Sep 26 2017

Formula

G.f.: 1/((1-3*x)*(1-x^3)). - Paul Barry, May 02 2003

a(n) = 3^(n+3)/26 -1/6 +(5*A049347(n)+7*A049347(n-1))/39. - R. J. Mathar, Mar 19 2011