A037480 Base-3 digits are, in order, the first n terms of the periodic sequence with initial period 1,2.

1, 5, 16, 50, 151, 455, 1366, 4100, 12301, 36905, 110716, 332150, 996451, 2989355, 8968066, 26904200, 80712601, 242137805, 726413416, 2179240250, 6537720751, 19613162255, 58839486766, 176518460300, 529555380901

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (3,1,-3).

Programs

Maple

a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=2*a[n-1]+3*a[n-2]+3 od: seq(a[n], n=1..33); # Zerinvary Lajos, Dec 14 2008

Mathematica

CoefficientList[Series[(2 x + 1)/((x - 1) (x + 1) (3 x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, May 01 2014 *)
Table[FromDigits[PadRight[{},n,{1,2}],3],{n,30}] (* or *) LinearRecurrence[ {3,1,-3},{1,5,16},30] (* Harvey P. Dale, Dec 15 2019 *)

PARI

Vec(x*(2*x+1)/((x-1)*(x+1)*(3*x-1)) + O(x^100)) \\ Colin Barker, Apr 30 2014

Formula

a(n) = (5*3^n + (-1)^n - 6)/8 . - Paul D. Hanna, Sep 23 2007

a(n) = 3*a(n-1)+a(n-2)-3*a(n-3). G.f.: x*(2*x+1) / ((x-1)*(x+1)*(3*x-1)). - Colin Barker, Apr 30 2014