A260998 Maximal size of a subset of Z_n with distinct sums of pairs (of distinct elements).

1, 2, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10

Offset

1,2

Links

Fausto A. C. Cariboni, Table of n, a(n) for n = 1..254

Fausto A. C. Cariboni, S_2-sets that yield a(n) for n = 2..254, Mar 24 2018.

H. Haanpaa, A. Huima and Patric R. J. Östergård, Sets in Z_n with Distinct Sums of Pairs, in Optimal discrete structures and algorithms (ODSA 2000). Discrete Appl. Math. 138 (2004), no. 1-2, 99-106. [Annotated scanned copies of four pages only from preprint of paper]

H. Haanpaa, A. Huima and Patric R. J. Östergård, Sets in Z_n with Distinct Sums of Pairs, in Optimal discrete structures and algorithms (ODSA 2000). Discrete Appl. Math. 138 (2004), no. 1-2, 99-106.

Formula

By the pigeonhole principle, C(a(n),2) <= n, yielding upper bound a(n) <= floor((1+sqrt(8*n+1))/2). - Rob Pratt, Nov 27 2017

Crossrefs

Cf. A004135, A004136, A260999.

Sequence in context: A117806 A351115 A085423 * A361110 A324728 A327008

Adjacent sequences: A260995 A260996 A260997 * A260999 A261000 A261001

Keyword

nonn

Author

N. J. A. Sloane, Aug 10 2015

Extensions

a(1)-a(90) from H. Haanpaa, A. Huima and Patric R. J. Östergård (see link), Nov 08 2000

a(1)-a(90) confirmed by Fausto A. C. Cariboni, Nov 09 2017

Status

approved