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

0,5

Comments

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

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).

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

Example

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

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 *)

Prog

(Magma) [3^(Floor(n/4)):n in [0..50]]; // Vincenzo Librandi, Sep 20 2011
(PARI) a(n)=3^(n\4) \\ Charles R Greathouse IV, Oct 03 2016

Crossrefs

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

Sequence in context: A203564 A369716 A365345 * A161836 A087576 A337328

Adjacent sequences: A111572 A111573 A111574 * A111576 A111577 A111578

Keyword

nonn,easy

Author

Jeremy Gardiner, Nov 17 2005

Status

approved