A033130 Base-3 digits are, in order, the first n terms of the periodic sequence with initial period 1,1,0.

1, 4, 12, 37, 112, 336, 1009, 3028, 9084, 27253, 81760, 245280, 735841, 2207524, 6622572, 19867717, 59603152, 178809456, 536428369, 1609285108, 4827855324, 14483565973, 43450697920, 130352093760, 391056281281, 1173168843844, 3519506531532, 10558519594597

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

Mathematica

Module[{nn=30, c}, c=PadRight[{}, nn, {1, 1, 0}]; Table[FromDigits[Take[c, n], 3], {n, nn}]] (* or *) LinearRecurrence[{3, 0, 1, -3}, {1, 4, 12, 37}, 30] (* Harvey P. Dale, Sep 01 2015 *)

Prog

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

Crossrefs

Sequence in context: A349053 A279277 A101555 * A196918 A099098 A019481

Adjacent sequences: A033127 A033128 A033129 * A033131 A033132 A033133

Keyword

nonn,base,easy

Author

Clark Kimberling

Status

approved