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Search: id:A124811
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| A124811 |
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Number of 4-ary Lyndon words of length n with exactly three 1s. |
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5
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| 3, 18, 89, 405, 1701, 6801, 26244, 98415, 360846, 1299078, 4605822, 16120350, 55801305, 191318760, 650483703, 2195382771, 7360989291, 24536630727, 81358302690, 268482398877, 882156452724, 2887057484028, 9414317882700
(list; graph; listen)
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OFFSET
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4,1
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FORMULA
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o.g.f. x^4 (3-9 x+8 x^2)/(1-3x)/(1-3x^3) = 1/3*((x/(1-3*x))^3 - x^3/(1-3*x^3)) a(n) = 1/3*sum_{d|3,d|n} mu(d) C(n/d-1,(n-3)/d )*3^((n-3)/d) = 1/3*C(n-1,2)*3^(n-3) if d=1,2 mod 3 = 1/3*C(n-1,2)*3^(n-3) - 1/3*3^((n-3)/3) if d=0 mod 3
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EXAMPLE
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a(5) = 18 because 111ab and 11a1b are Lyndon of length 4 for ab=2,3,4
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CROSSREFS
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Cf. A124810, A124812, A124813, A124814, A001840, A124721.
Sequence in context: A103897 A119424 A037295 this_sequence A006568 A147518 A088336
Adjacent sequences: A124808 A124809 A124810 this_sequence A124812 A124813 A124814
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KEYWORD
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nonn
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AUTHOR
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Mike Zabrocki (zabrocki(AT)mathstat.yorku.ca), Nov 08 2006
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