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A158449
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The number of sigma-admissible subsets of {1,2,...,n} as defined by Marzuola-Miller.
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3
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1, 0, 1, 0, 2, 0, 3, 1, 7, 3, 17, 7, 43, 24, 118, 74, 330, 206, 888, 612, 2571, 1810, 7274, 5552, 21099, 16334, 61252, 49025, 179239, 146048, 523455, 440980, 1554184, 1315927, 4572794, 3972193, 13569220, 11873290, 40263681, 35824869, 119901609, 107397585
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OFFSET
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1,5
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COMMENTS
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a(n), or Asigma(n), equals the number of sigma-admissible subsets of {1,2,...,n}.
Alternate description: (1) Asigma(k) is the same as the number of additive 2-bases for k which are not additive 2-bases for k+1. (2) Asigma(n) is the number of vertices at height n in the rooted tree in figure 5 of [Marzuola-Miller] which spawn only one vertex at height n+1. [Jeremy L. Marzuola (marzuola(AT)math.uni-bonn.de), Aug 08 2009]
The number of symmetric numerical sets S with atom monoid A(S) equal to {0,n+1,2n+2,2n+3,2n+4,2n+5,...}
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LINKS
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FORMULA
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Recursively related to A164047 by the formula Asigma(2k+1)' = 2Asigma(2k)'-Asigma(k)
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EXAMPLE
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a(1)=a(3)=1 since {0,2,4,5,6,7,...} and {0,1,4,5,8,9,10,11,...} are the only sets satisfying the required conditions.
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PROG
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(C) See Martin Fuller link
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Definition rephrased by Jeremy L. Marzuola (marzuola(AT)math.uni-bonn.de), Aug 08 2009
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STATUS
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approved
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