A222807 Number of subsets A of {0,1,...,n-1} with |A+A| > |A-A|.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 10, 30, 66, 144, 314, 692, 1452, 3046, 6388, 13298, 27274, 56164, 113672, 231892, 470984, 950178, 1912700, 3868034, 7772172, 15651674, 31464544, 63154106, 126603428, 254088618, 508541874, 1018817124

Offset

1,15

Comments

Some authors work with subsets of [0..n-1], others with subsets of [1..n].

Keywords: sum-dominant sets, MSTD sets.

a(1)-a(21) were computed by Daniel C. R. Scheinerman, Mar 10 2013; although a(1)-a(27) had been found by Kevin O'Bryant some time earlier.

Links

Table of n, a(n) for n = 1..41

Greg Martin and Kevin O'Bryant, Many sets have more sums than differences, arXiv:math/0608131 [math.NT], 2006.

D. Penman and M. Wells, On Sets with More Restricted Sums than Differences, Integers, Vol. 13 (2013), A57.

Formula

a(n) = Sum_{i=1..n} (n-i+1)*A224893(i).

Example

The four examples illustrating a(15)=4 are (cf. A140794):
0    2    3    7   10   11   12   14,
0    2    3    4    7   11   12   14,
0    1    2    5    9   10   12   13   14,
0    1    2    4    5    9   12   13   14.

Crossrefs

Cf. A118544, A140794, A222808, A224893.

Sequence in context: A048044 A047188 A002220 * A090578 A007713 A058488

Adjacent sequences: A222804 A222805 A222806 * A222808 A222809 A222810

Keyword

nonn,more

Author

N. J. A. Sloane, Mar 10 2013

Extensions

a(28)-a(35) from James Wilcox, Jul 22 2013

a(36)-a(40) from Giovanni Resta, Jul 23 2013

a(41) from James Wilcox, Jul 24 2013

Status

approved