
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 nonoverlapping 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^n1)/2)*(n+1)*n^((n1)/2) >= a(n) >= 2^((1/2)*n*log(n)n*(2+o(1))) [Alon&Vu].  Andrey Zabolotskiy, Oct 23 2017


LINKS

Table of n, a(n) for n=1..6.
Noga Alon, Dmitry N. Kozlov, Coins with Arbitrary Weights, Journal of Algorithms, Volume 25, Issue 1, October 1997, Pages 162176.
Noga Alon, Van H. Vu, AntiHadamard Matrices, Coin Weighing, Threshold Gates, and Indecomposable Hypergraphs, Journal of Combinatorial Theory, Series A, Volume 79, Issue 1, July 1997, Pages 133160.
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 114 [gives lower bounds for a(n) up to n=15].
