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A222807 Number of subsets A of {0,1,...,n-1} with |A+A| > |A-A|. 8
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A048044 A047188 A002220 * A090578 A007713 A058488
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

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Last modified April 18 04:56 EDT 2024. Contains 371767 sequences. (Running on oeis4.)