%I #46 Feb 02 2020 21:36:31

%S 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,

%T 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,

%U 8,8,8,8,9,8,8,8,8,8,8,9,8,8,8,8

%N Maximal size of a subset of Z_n with distinct sums of any two elements.

%H Fausto A. C. Cariboni, <a href="/A260999/b260999.txt">Table of n, a(n) for n = 1..295</a>

%H Fausto A. C. Cariboni, <a href="/A260999/a260999_2.txt">Sets that yield a(n) for n = 2..295</a>, Jan 27 2018.

%H H. Haanpaa, A. Huima and Patric R. J. Östergård, <a href="/A004135/a004135.pdf">Sets in Z_n with Distinct Sums of Pairs</a>, 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 H. Haanpaa, A. Huima and Patric R. J. Östergård, <a href="https://doi.org/10.1016/S0166-218X(03)00273-7">Sets in Z_n with Distinct Sums of Pairs</a>, in Optimal discrete structures and algorithms (ODSA 2000). Discrete Appl. Math. 138 (2004), no. 1-2, 99-106.

%F 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

%Y Cf. A004135, A004136, A260998.

%K nonn

%O 1,3

%A _N. J. A. Sloane_, Aug 10 2015

%E More terms from _Rob Pratt_, Nov 27 2017