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%I #56 Feb 02 2020 21:36:21
%S 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,
%T 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,
%U 9,9,9,10,10,10,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10
%N Maximal size of a subset of Z_n with distinct sums of pairs (of distinct elements).
%H Fausto A. C. Cariboni, <a href="/A260998/b260998.txt">Table of n, a(n) for n = 1..254</a>
%H Fausto A. C. Cariboni, <a href="/A260998/a260998_2.txt">S_2-sets that yield a(n) for n = 2..254</a>, Mar 24 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),2) <= n, yielding upper bound a(n) <= floor((1+sqrt(8*n+1))/2). - _Rob Pratt_, Nov 27 2017
%Y Cf. A004135, A004136, A260999.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Aug 10 2015
%E a(1)-a(90) from H. Haanpaa, A. Huima and Patric R. J. Östergård (see link), Nov 08 2000
%E a(1)-a(90) confirmed by _Fausto A. C. Cariboni_, Nov 09 2017
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