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A158449 The number of sigma-admissible subsets of {1,2,...,n} as defined by Marzuola-Miller. 1


%S 1,0,1,0,2,0,3,1,7,3,17,7,43,24,118,74,330,206,888,612,2571,1810,7274,

%T 5552,21099,16334,61252,49025,179239,146048,523455,440980

%N The number of sigma-admissible subsets of {1,2,...,n} as defined by Marzuola-Miller.

%C a(n), or Asigma(n), equals the number of sigma-admissible subsets of {1,2,...,n}.

%C 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]

%C 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,...}

%H S. R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/">Monoids of natural numbers</a>

%H S. R. Finch, <a href="/A066062/a066062.pdf">Monoids of natural numbers</a>, March 17, 2009. [Cached copy, with permission of the author]

%H J. Marzuola and A. Miller, <a href="http://arxiv.org/abs/0805.3493">Counting Numerical Sets with No Small Atoms</a>, arXiv:0805.3493 [math.CO], 2008.

%H J. Marzuola and A. Miller, <a href="https://doi.org/10.1016/j.jcta.2010.03.002">Counting numerical sets with no small atoms</a>, J. Combin. Theory A 117 (6) (2010) 650-667.

%F Recursively related to A164047 by the formula Asigma(2k+1)' = 2Asigma(2k)'-Asigma(k)

%e 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.

%Y Cf. A066062, A164047.

%K nonn,more

%O 1,5

%A _Steven Finch_, Mar 19 2009

%E Definition rephrased by Jeremy L. Marzuola (marzuola(AT)math.uni-bonn.de), Aug 08 2009

%E Edited by _R. J. Mathar_, Aug 31 2009

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Last modified September 21 19:57 EDT 2020. Contains 337273 sequences. (Running on oeis4.)