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 A158449 The number of sigma-admissible subsets of {1,2,...,n} as defined by Marzuola-Miller. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS 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,...} LINKS 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. FORMULA Recursively related to A164047 by the formula Asigma(2k+1)' = 2Asigma(2k)'-Asigma(k) EXAMPLE 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. CROSSREFS Cf. A066062, A164047. Sequence in context: A350962 A241644 A241640 * A106533 A192421 A035223 Adjacent sequences:  A158446 A158447 A158448 * A158450 A158451 A158452 KEYWORD nonn,more AUTHOR Steven Finch, Mar 19 2009 EXTENSIONS Definition rephrased by Jeremy L. Marzuola (marzuola(AT)math.uni-bonn.de), Aug 08 2009 Edited by R. J. Mathar, Aug 31 2009 STATUS approved

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Last modified May 26 10:17 EDT 2022. Contains 354086 sequences. (Running on oeis4.)