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Search: id:A074650
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| A074650 |
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Table T(n,k) by antidiagonals. Number of Lyndon words (aperiodic necklaces) with n beads of k colors. |
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18
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| 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)
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OFFSET
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1,2
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REFERENCES
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F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, pg 97 (2.3.74)
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LINKS
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Index entries for sequences related to Lyndon words
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FORMULA
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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
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EXAMPLE
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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 ...
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MAPLE
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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
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CROSSREFS
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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
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KEYWORD
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nonn,tabl
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AUTHOR
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Christian G. Bower (bowerc(AT)usa.net), Aug 28 2002
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