A033121 Base-3 digits are, in order, the first n terms of the periodic sequence with initial period 1,0,1.

1, 3, 10, 31, 93, 280, 841, 2523, 7570, 22711, 68133, 204400, 613201, 1839603, 5518810, 16556431, 49669293, 149007880, 447023641, 1341070923, 4023212770, 12069638311, 36208914933, 108626744800, 325880234401, 977640703203, 2932922109610, 8798766328831

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (3,0,1,-3).

Formula

a(n) = 3*a(n-1) + a(n-3) - 3*a(n-4).

G.f.: x*(1+x^2) / ((1-x)*(1-3*x)*(1+x+x^2)). - Colin Barker, Dec 24 2015

a(n) = floor(5*3^n/13). - Christian Krause, May 18 2026

a(n) = A033139(n) + A033139(n-2). - R. J. Mathar, Jun 11 2026

Mathematica

Table[FromDigits[PadRight[{}, n, {1, 0, 1}], 3], {n, 30}] (* Harvey P. Dale, Jan 20 2017 *)
(* Alternative: *)
LinearRecurrence[ {3, 0, 1, -3}, {1, 3, 10, 31}, 30] (* Harvey P. Dale, Jan 20 2017 *)

Prog

(PARI) Vec(x*(1+x^2)/((1-x)*(1-3*x)*(1+x+x^2)) + O(x^30)) \\ Colin Barker, Dec 24 2015

Crossrefs

Sequence in context: A212031 A339032 A374925 * A180432 A237930 A192337

Adjacent sequences: A033118 A033119 A033120 * A033122 A033123 A033124

Keyword

nonn,base,easy,changed

Author

Clark Kimberling

Status

approved