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A051841
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Number of binary Lyndon words with an even number of 1's.
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12
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1, 0, 1, 1, 3, 4, 9, 14, 28, 48, 93, 165, 315, 576, 1091, 2032, 3855, 7252, 13797, 26163, 49929, 95232, 182361, 349350, 671088, 1290240, 2485504, 4792905, 9256395, 17894588, 34636833, 67106816
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| Also number of trace 0 irreducible polynomials over GF(2).
Also number of trace 0 Lyndon words over GF(2).
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..300
Index entries for sequences related to Lyndon words
F. Ruskey, Number of q-ary Lyndon words with given trace mod q
F. Ruskey, Number of Lyndon words of given trace
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FORMULA
| ( Sum_{d|n} gcd(d, 2)*mu(d)*2^{n/d}) / (2n)
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EXAMPLE
| a(5)= 3 = |{ 00011, 00101, 01111 }|
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CROSSREFS
| Same as A001037 - A000048. Same as A042980 + A042979.
Sequence in context: A002823 A109509 A006053 * A096081 A054162 A174783
Adjacent sequences: A051838 A051839 A051840 * A051842 A051843 A051844
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KEYWORD
| nonn,easy,nice
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AUTHOR
| Frank Ruskey (ruskey(AT)cs.uvic.ca), Dec 13 1999
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