|
|
A127975
|
|
Repeat 3^n three times.
|
|
6
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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
|
|
|
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
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|