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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,...}

REFERENCES

J. Marzuola and A. Miller, "Counting numerical sets with no small atoms", To appear in Journal of Combinatorial Theory: A.

LINKS

Table of n, a(n) for n=1..32.

S. R. Finch, Monoids of natural numbers

J. Marzuola and A. Miller, Counting numerical sets with no small atoms arXiv:0805.3493.

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: A143351 A241644 A241640 * A106533 A192421 A035223

Adjacent sequences:  A158446 A158447 A158448 * A158450 A158451 A158452

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

STATUS

approved

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Last modified December 10 21:42 EST 2016. Contains 279011 sequences.