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

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Index entries for linear recurrences with constant coefficients, signature (3,1,-3).

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

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 *)

Prog

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

Crossrefs

Sequence in context: A082001 A084356 A007806 * A027108 A304168 A317817

Adjacent sequences: A037477 A037478 A037479 * A037481 A037482 A037483

Keyword

nonn,base,easy

Author

Clark Kimberling

Status

approved