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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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1
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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
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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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Table of n, a(n) for n=1..32.
S. R. Finch, Monoids of natural numbers
S. R. Finch, Monoids of natural numbers, March 17, 2009. [Cached copy, with permission of the author]
J. Marzuola and A. Miller, Counting Numerical Sets with No Small Atoms, arXiv:0805.3493 [math.CO], 2008.
J. Marzuola and A. Miller, Counting numerical sets with no small atoms, J. Combin. Theory A 117 (6) (2010) 650-667.
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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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CROSSREFS
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Cf. A066062, A164047.
Sequence in context: A350962 A241644 A241640 * A106533 A192421 A035223
Adjacent sequences: A158446 A158447 A158448 * A158450 A158451 A158452
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KEYWORD
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nonn,more
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AUTHOR
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Steven Finch, Mar 19 2009
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EXTENSIONS
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Definition rephrased by Jeremy L. Marzuola (marzuola(AT)math.uni-bonn.de), Aug 08 2009
Edited by R. J. Mathar, Aug 31 2009
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STATUS
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approved
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