

A158449


The number of sigmaadmissible subsets of {1,2,...,n} as defined by MarzuolaMiller.


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
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OFFSET

1,5


COMMENTS

a(n), or Asigma(n), equals the number of sigmaadmissible subsets of {1,2,...,n}.
Alternate description: (1) Asigma(k) is the same as the number of additive 2bases for k which are not additive 2bases for k+1. (2) Asigma(n) is the number of vertices at height n in the rooted tree in figure 5 of [MarzuolaMiller] which spawn only one vertex at height n+1. [Jeremy L. Marzuola (marzuola(AT)math.unibonn.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

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) 650667.


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.unibonn.de), Aug 08 2009
Edited by R. J. Mathar, Aug 31 2009


STATUS

approved



