A111575 Powers of 3 repeated four times.

1, 1, 1, 1, 3, 3, 3, 3, 9, 9, 9, 9, 27, 27, 27, 27, 81, 81, 81, 81, 243, 243, 243, 243, 729, 729, 729, 729, 2187, 2187, 2187, 2187, 6561, 6561, 6561, 6561, 19683, 19683, 19683, 19683, 59049, 59049, 59049, 59049, 177147, 177147, 177147, 177147, 531441

Offset: 0

Author

Jeremy Gardiner, Nov 17 2005

Keywords

• nonn
• easy

Comments

Generating sequence for the number of 0's and 1's (run lengths) in the parity of A006072, A111065 and A118594.

Examples

			a(10) = 3^floor(10/4) = 3^2 = 9.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..8000
• Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 3).

Crossrefs

Cf. A006072, A111065, A108411, A118594, A127975.

Programs

Magma

[3^(Floor(n/4)):n in [0..50]]; // Vincenzo Librandi, Sep 20 2011

Mathematica

With[{pt=3^Range[0,15]},Sort[Join[pt,pt,pt,pt]]] (* Harvey P. Dale, Sep 17 2011 *)
Table[PadRight[{},4,3^n],{n,0,15}]//Flatten (* Harvey P. Dale, Jan 17 2019 *)

PARI

a(n)=3^(n\4) \\ Charles R Greathouse IV, Oct 03 2016

Formula

a(n) = 3^floor(n/4).

O.g.f.: -(1+x)*(1+x^2)/(-1+3*x^4). - R. J. Mathar, Jan 08 2008