OFFSET
1,1
COMMENTS
This sequence arises in the following problem: Given a set of binary elements (e.g., coins that may have one of the two weights), determine whether all of them are the same by weighing equally sized non-overlapping subsets n times. a(n) is the maximum size of a set whose integrity can be checked with n weighings.
The next terms are probably a(7) = 2234 and a(8) = 9966 (from the Kozlov/Vu reference). - Konstantin Knop, Oct 18 2017
((3^n-1)/2)*(n+1)*n^((n-1)/2) >= a(n) >= 2^((1/2)*n*log(n)-n*(2+o(1))) [Alon&Vu]. - Andrey Zabolotskiy, Oct 23 2017
LINKS
Noga Alon, Dmitry N. Kozlov, Coins with Arbitrary Weights, Journal of Algorithms, Volume 25, Issue 1, October 1997, Pages 162-176.
Noga Alon, Van H. Vu, Anti-Hadamard Matrices, Coin Weighing, Threshold Gates, and Indecomposable Hypergraphs, Journal of Combinatorial Theory, Series A, Volume 79, Issue 1, July 1997, Pages 133-160.
IBM Research, Ponder This December 2016 challenge
IBM Research, Solutions for n=4 and 5
Dmitry N. Kozlov, Van H. Vu, Coins and Cones, Journal of Combinatorial Theory, Series A, Volume 78, Issue 1, April 1997, Pages 1-14 [gives lower bounds for a(n) up to n=15].
CROSSREFS
KEYWORD
nonn,more,hard
AUTHOR
Serge Batalov, Jan 02 2017
STATUS
approved