%I #28 Feb 26 2024 01:59:03

%S 1,1,1,3,3,3,9,9,9,27,27,27,81,81,81,243,243,243,729,729,729,2187,

%T 2187,2187,6561,6561,6561,19683,19683,19683,59049,59049,59049,177147,

%U 177147,177147,531441,531441,531441,1594323,1594323,1594323,4782969,4782969,4782969

%N Repeat 3^n three times.

%C 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

%H Vincenzo Librandi, <a href="/A127975/b127975.txt">Table of n, a(n) for n = 0..6000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,3).

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

%e 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

%p seq(3^floor(n/3),n=0..45); # _Dennis P. Walsh_, Sep 06 2018

%t 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 *)

%o (Magma) [3^(Floor(n/3)):n in [0..50]]; // _Vincenzo Librandi_, Sep 20 2011

%o (PARI) a(n)=3^(n\3) \\ _Charles R Greathouse IV_, Oct 03 2016

%Y Cf. A108411, A111575.

%K nonn,easy

%O 0,4

%A _Paul Barry_, Feb 09 2007

%E Edited and corrected by _R. J. Mathar_, Jun 14 2008