|
|
A214944
|
|
Number of squarefree words of length 5 in an (n+1)-ary alphabet.
|
|
1
|
|
|
0, 30, 264, 1140, 3480, 8610, 18480, 35784, 64080, 107910, 172920, 265980, 395304, 570570, 803040, 1105680, 1493280, 1982574, 2592360, 3343620, 4259640, 5366130, 6691344, 8266200, 10124400, 12302550, 14840280, 17780364, 21168840, 25055130
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
Empirical: a(n) = n^5 + n^4 - 2*n^3 - n^2 + n.
G.f.: 6*x^2*(5 + 14*x + x^2) / (1 - x)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
(End)
|
|
EXAMPLE
|
Some solutions for n=2:
..1....2....2....0....1....0....0....0....2....1....2....2....0....2....1....2
..2....1....1....1....0....1....2....2....1....0....0....0....1....1....2....0
..0....0....2....2....2....2....1....0....0....2....1....1....0....2....0....2
..2....2....0....0....1....0....0....1....1....0....2....2....2....0....1....1
..1....1....2....2....2....1....2....0....2....1....0....1....0....1....0....0
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|