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A066062
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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.
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5
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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; internal format)
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OFFSET
| 0,3
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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.
Contribution from S. R. Finch (Steven.Finch(AT)inria.fr), 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)
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LINKS
| S. R. Finch, Monoids of natural numbers
J. Marzuola and A. Miller, Counting numerical sets with no small atoms. [From S. R. Finch (Steven.Finch(AT)inria.fr), Mar 15 2009]
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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.
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CROSSREFS
| A008929, A066063
Cf. A158291 [From S. R. Finch (Steven.Finch(AT)inria.fr), Mar 15 2009]
Sequence in context: A002215 A007562 A171682 * A008929 A164047 A158291
Adjacent sequences: A066059 A066060 A066061 * A066063 A066064 A066065
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KEYWORD
| nonn
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AUTHOR
| John W. Layman (layman(AT)math.vt.edu), Dec 01 2001
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