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A284841
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Number of primitive (aperiodic) palindromic structures of length n using an infinite alphabet.
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4
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1, 0, 1, 1, 4, 3, 14, 13, 50, 47, 202, 197, 876, 862, 4134, 4125, 21146, 21092, 115974, 115922, 678554, 678367, 4213596, 4213381, 27644432, 27643560, 190899270, 190898444, 1382958544, 1382954355, 10480142146, 10480138007, 82864869600, 82864848657
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OFFSET
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1,5
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COMMENTS
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Permuting the symbols will not change the structure.
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REFERENCES
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M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]
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LINKS
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FORMULA
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a(n) = Sum_{k=1..ceiling(n/2)} A284826(n,k).
a(n) = Sum_{d | n} mu(n/d) * Bell(ceiling(d/2)).
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EXAMPLE
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n = 1: a => 1
n = 3: aba => 1
n = 4: abba => 1
n = 5: aabaa, ababa, abbba, abcba => 4
n = 6: aabbaa, abbbba, abccba => 3
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MATHEMATICA
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a[n_] := DivisorSum[n, MoebiusMu[n/#] BellB[Ceiling[#/2]]&];
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PROG
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(PARI)
bell(n) = sum(k=0, n, stirling(n, k, 2));
a(n) = sumdiv(n, d, moebius(n/d) * bell(ceil(d/2)));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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