

A260999


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


4



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
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OFFSET

1,3


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 P. R. J. Ostergard, Sets in Z_n with Distinct Sums of Pairs, in Optimal discrete structures and algorithms (ODSA 2000). Discrete Appl. Math. 138 (2004), no. 12, 99106. [Annotated scanned copies of four pages only from preprint of paper]
H. Haanpaa, A. Huima and P. R. J. Ostergard, Sets in Z_n with Distinct Sums of Pairs, in Optimal discrete structures and algorithms (ODSA 2000). Discrete Appl. Math. 138 (2004), no. 12, 99106.


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


CROSSREFS

Cf. A004135, A004136, A260998.
Sequence in context: A064601 A023967 A278163 * A090532 A003058 A000194
Adjacent sequences: A260996 A260997 A260998 * A261000 A261001 A261002


KEYWORD

nonn,changed


AUTHOR

N. J. A. Sloane, Aug 10 2015


EXTENSIONS

More terms from Rob Pratt, Nov 27 2017


STATUS

approved



