A140794 -id:A140794 - cp's OEIS frontend

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

N. J. A. Sloane, Mar 10 2013

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.

			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.

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.

Cf. A118544, A140794, A222808, A224893.

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

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

A118544 Number of subsets A of {1,2,...,n} with |A+A| = |A-A|.

Original entry on oeis.org

2, 4, 8, 14, 24, 40, 66, 106, 174, 286, 480, 814, 1412, 2480, 4476, 8184, 15230, 28652, 54488, 104262, 201266, 390090, 760234, 1486030, 2914492, 5728506, 11289420, 22279222, 44046072, 87181188, 172777354, 342724456, 680524908, 1352154964, 2688763324

Offset: 1

Kevin O'Bryant, May 07 2006

nonn

Keywords: sum-dominant sets, MSTD sets.

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

			a(4)=14: two of the sixteen subsets of {1,2,3,4} have |A+A|<|A-A| (specifically, {1,3,4} and {1,2,4}).

James Wilcox and Giovanni Resta, Table of n, a(n) for n = 1..40 (first 35 terms from James Wilcox)

Cf. A222807, A222808, A140794.

a(21)-a(29) from Robert Gerbicz, Nov 19 2010

a(30)-a(35) from James Wilcox, Jul 22 2013

A222808 Number of subsets A of {0,1,...,n-1} with |A+A| < |A-A|.

Original entry on oeis.org

0, 0, 0, 2, 8, 24, 62, 150, 338, 738, 1568, 3282, 6780, 13904, 28288, 57342, 115812, 233426, 469656, 944000, 1895194, 3802762, 7625328, 15284798, 30626642, 61353084, 122872144, 246042562, 492592948, 986089652, 1973756116, 3950330140, 7905541650, 15819942048, 31655323370

Offset: 1

N. J. A. Sloane, Mar 10 2013

nonn

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.

James Wilcox and Giovanni Resta, Table of n, a(n) for n = 1..40 (first 35 terms from James Wilcox)
Greg Martin and Kevin O'Bryant, Many sets have more sums than differences, arXiv:math/0608131 [math.NT], 2006.

Cf. A118544, A140794, A222807.

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

A102282 Smallest possible example of an MSTD ("More sums than differences") set.

Original entry on oeis.org

0, 2, 3, 4, 7, 11, 12, 14

Offset: 1

N. J. A. Sloane, Sep 08 2008

Reflection of A140794: a(n) = 14 - A140794(9-n). - James Wilcox, Jul 24 2013

Hegarty, who attributes the set to Conway, proves its minimality. - Charles R Greathouse IV, Sep 26 2019

B. Hayes, Calculemus!, American Scientist, 96 (Sep-Oct 2008), 362-366.

Peter Hegarty, Some explicit constructions of sets with more sums than differences (2007)

Cf. A222807, A118544, A222808.

cp's OEIS Frontend

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

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A118544 Number of subsets A of {1,2,...,n} with |A+A| = |A-A|.

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A222808 Number of subsets A of {0,1,...,n-1} with |A+A| < |A-A|.

Views

Author

Keywords

Comments

Links

Crossrefs

Extensions

A102282 Smallest possible example of an MSTD ("More sums than differences") set.

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