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Search: id:A082951
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| A082951 |
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Number of primitive (aperiodic) word structures of length n using an infinite alphabet. |
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+0
2
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| 1, 1, 4, 13, 51, 197, 876, 4125, 21142, 115922, 678569, 4213381, 27644436, 190898444, 1382958489, 10480138007, 82864869803, 682076784814, 5832742205056, 51724158119384, 474869816155870, 4506715737768752
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Permuting the alphabet will not change a word structure. Thus aabc and bbca have the same structure.
Row sums of triangle A137651 - Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 01 2008
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FORMULA
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a(n)=sum mu(c)*A000110(d) over all cd=n; equivalently, A000110(n) = sum a(k), where the sum is over all k|n
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EXAMPLE
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There are A000110(3)=5 word structures of length 3: aaa, aab, aba, abb, abc. The first consists of 3 copies of a word of length 1; the other 4 are primitive. So a(3)=4.
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MAPLE
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with(combinat, bell): with(numtheory): newb := proc(n) local s, i; s := 0; for i in divisors(n) do s := s+bell(i)*mobius(n/i): end do: end proc;
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CROSSREFS
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Cf. A000110, A056277, A056272, A056275, A056274, A056278.
Cf. A137651.
Sequence in context: A002746 A056276 A056277 this_sequence A135345 A097169 A129147
Adjacent sequences: A082948 A082949 A082950 this_sequence A082952 A082953 A082954
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KEYWORD
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easy,nonn
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AUTHOR
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Vadim Ponomarenko (vadim123(AT)gmail.com), May 26 2003
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