A127975 Repeat 3^n three times.

1, 1, 1, 3, 3, 3, 9, 9, 9, 27, 27, 27, 81, 81, 81, 243, 243, 243, 729, 729, 729, 2187, 2187, 2187, 6561, 6561, 6561, 19683, 19683, 19683, 59049, 59049, 59049, 177147, 177147, 177147, 531441, 531441, 531441, 1594323, 1594323, 1594323, 4782969, 4782969, 4782969

Offset

0,4

Comments

a(n) is the number of functions f:[n+1]->[3] with f(1)=1 and with f(x)=f(y) whenever y=ceiling(x/3). - Dennis P. Walsh, Sep 06 2018

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..6000

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

Formula

G.f.: (1+x+x^2)/(1-3*x^3).

Example

a(6)=9 since there are exactly 9 functions f:[7]->[3], denoted by <f(1),f(2),...,f(7)>, with f(1)=1 and with f(x)=f(y) whenever y=ceiling(x/3). The nine functions are <1,1,1,1,1,1,1>, <1,1,1,1,1,1,2>, <1,1,1,1,1,1,3>, <1,1,1,2,2,2,1>, <1,1,1,2,2,2,2>, <1,1,1,2,2,2,3>, <1,1,1,3,3,3,1>, <1,1,1,3,3,3,2>, and <1,1,1,3,3,3,3>. - Dennis P. Walsh, Sep 06 2018

Maple

seq(3^floor(n/3), n=0..45); # Dennis P. Walsh, Sep 06 2018

Mathematica

CoefficientList[Series[(1+x+x^2)/(1-3*x^3), {x, 0, 50}], x] (* or *) Table[3^(Floor[n/3]), {n, 0, 50}] (* G. C. Greubel, Apr 30 2017 *)

Prog

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

Crossrefs

Cf. A108411, A111575.

Sequence in context: A132171 A304682 A217645 * A060828 A332337 A161808

Adjacent sequences: A127972 A127973 A127974 * A127976 A127977 A127978

Keyword

nonn,easy

Author

Paul Barry, Feb 09 2007

Extensions

Edited and corrected by R. J. Mathar, Jun 14 2008

Status

approved