|
Search: id:A074650
|
|
|
| A074650 |
|
Table T(n,k) by antidiagonals. Number of Lyndon words (aperiodic necklaces) with n beads of k colors. |
|
+0
18
|
|
| 1, 2, 0, 3, 1, 0, 4, 3, 2, 0, 5, 6, 8, 3, 0, 6, 10, 20, 18, 6, 0, 7, 15, 40, 60, 48, 9, 0, 8, 21, 70, 150, 204, 116, 18, 0, 9, 28, 112, 315, 624, 670, 312, 30, 0, 10, 36, 168, 588, 1554, 2580, 2340, 810, 56, 0, 11, 45, 240, 1008, 3360, 7735, 11160, 8160, 2184, 99, 0, 12
(list; table; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
REFERENCES
|
F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, pg 97 (2.3.74)
|
|
LINKS
|
Index entries for sequences related to Lyndon words
|
|
FORMULA
|
T(n, k) = (1/n) * Sum ( mu(n/d)*k^d ), d|n
T(n, k) = ( k^n - Sum_{d<n,d|n} d*T(d,k) ) / n - Alois P. Heinz (heinz(AT)hs-heilbronn.de), Mar 28 2008
|
|
EXAMPLE
|
1 2 3 4 5 ...
0 1 3 6 10 ...
0 2 8 20 40 ...
0 3 18 60 150 ...
0 6 48 204 624 ...
|
|
MAPLE
|
with (numtheory): T := proc (n, k) add(mobius(n/d)*k^d, d=divisors(n))/n end; seq (seq(T(i, d-i), i=1..d-1), d=2..12); - Alois P. Heinz (heinz(AT)hs-heilbronn.de), Mar 28 2008
|
|
CROSSREFS
|
Columns 2-12: A001037, A027376, A027377, A001692, A032164, A001693, A027380, A027381, A032165, A032166, A032167.
Rows 1-4: A000027, A000217(n-1), A007290(n+1), A006011.
Diagonal: A075147.
See also A102659.
Sequence in context: A098862 A003988 A144257 this_sequence A144955 A002187 A124756
Adjacent sequences: A074647 A074648 A074649 this_sequence A074651 A074652 A074653
|
|
KEYWORD
|
nonn,tabl
|
|
AUTHOR
|
Christian G. Bower (bowerc(AT)usa.net), Aug 28 2002
|
|
|
Search completed in 0.003 seconds
|
