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A066062 Number of distinct subsets S of T={0,1,2,...,n} such that each element of T is the sum of two elements of S. 7
1, 1, 2, 3, 6, 10, 20, 37, 73, 139, 275, 533, 1059, 2075, 4126, 8134, 16194, 32058, 63910, 126932, 253252, 503933, 1006056, 2004838, 4004124, 7987149, 15957964 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

This sequence may be equivalent to A008929, but has a somewhat different definition. The size of the smallest subset counted by this sequence, for a given n, is given in A066063.

From Steven Finch, Mar 15 2009: (Start)

Such sets S are called additive 2-bases for {0,1,2,...,n}.

a(n) is also the number of symmetric numerical sets S with atom monoid A(S) equal to {0, 2n+2, 2n+3, 2n+4, 2n+5, ...}. (End)

LINKS

Table of n, a(n) for n=0..26.

S. R. Finch, Monoids of natural numbers, March 17, 2009. [Cached copy, with permission of the author]

G. Grekos, L. Haddad, C. Helou, and J. Pihko, On the Erdos-TurĂ¡n conjecture, J. Number Theory 102 (2003), no. 2, 339-352.

J. Marzuola and A. Miller, Counting numerical sets with no small atoms, arXiv:0805.3493 [math.CO], 2008. - Steven Finch, Mar 15 2009

EXAMPLE

For n=2, the definition obviously requires that S contain both 0 and 1. The only subsets of {0,1,2} that do this are {0,1} and {0,1,2}. For both of these, we have 0=0+0, 1=0+1, 2=1+1, so a(2)=2.

CROSSREFS

Cf. A008929, A066063.

Cf. A158291. - Steven Finch, Mar 15 2009

Sequence in context: A007562 A222855 A171682 * A008929 A164047 A158291

Adjacent sequences:  A066059 A066060 A066061 * A066063 A066064 A066065

KEYWORD

nonn,more

AUTHOR

John W. Layman, Dec 01 2001

STATUS

approved

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Last modified November 18 10:38 EST 2017. Contains 294887 sequences.