A260999 Maximal size of a subset of Z_n with distinct sums of any two elements.
1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 9, 8, 8, 8, 8
Offset: 1
Keywords
Links
- Fausto A. C. Cariboni, Table of n, a(n) for n = 1..295
- Fausto A. C. Cariboni, Sets that yield a(n) for n = 2..295, Jan 27 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)+1,2) <= n, yielding upper bound a(n) <= floor((-1+sqrt(8*n+1))/2). - Rob Pratt, Nov 27 2017
Extensions
More terms from Rob Pratt, Nov 27 2017