login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 13
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-Turán 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

J. Marzuola and A. Miller, Counting numerical sets with no small atoms, J. Combin. Theory A 117 (6) (2010) 650-667.

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.

MATHEMATICA

a[n_] := Module[{},

  T = Range[0, n];

  ST = Subsets[T, {Floor[n^(2/3)], n+1}];

  selQ[S_] := Intersection[T, Total /@ Tuples[S, {2}]] == T;

  SST = Select[ST, selQ]; min = Min[Length /@ SST];

  SST // Length

];

Table[an = a[n]; Print["a(", n, ") = ", an, " min = ", min]; an, {n, 0, 24}] (* Jean-François Alcover, Nov 05 2018 *)

CROSSREFS

Cf. A008929, A066063.

Cf. A158291. - Steven Finch, Mar 15 2009

Sequence in context: A329702 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 27 21:52 EDT 2020. Contains 334671 sequences. (Running on oeis4.)