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
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Feb 09 2007
EXTENSIONS
Edited and corrected by R. J. Mathar, Jun 14 2008
STATUS
approved