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
Martin Fuller, Table of n, a(n) for n = 1..65
S. R. Finch, Monoids of natural numbers [Broken link]
S. R. Finch, Monoids of natural numbers, March 17, 2009. [Cached copy, with permission of the author]
Martin Fuller, C program
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.
PROG
(C) See Martin Fuller link
CROSSREFS
KEYWORD
nonn
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
a(33) onwards from Martin Fuller, Sep 13 2023
STATUS
approved