A292836 - OEIS

%I #20 Apr 07 2024 17:42:47

%S 0,1,1,3,3,4,4,6,7,7,8,10,10,11,11,13,14,14,15,17,17,18,18,20,21,22,

%T 23,24,24,25,26,28,29,29,30,31,32,33,33,35,36,37,38,39,39,40,41,43,44,

%U 44,45,46,47,48,48,50,51,52,53,54,54,55,56,58,59,59,60,62,62

%N a(n) is the minimum number of steps to a terminal state during the following procedure: start with n piles each containing one stone; any number of stones can be transferred between piles of equal size.

%C A terminal state is one in which all pile sizes are different, that is, there are no legal remaining ways to move stones.

%C A121924 is the analogous sequence for when only one stone can be moved at a time.

%C A011371 is the analogous sequence for when all stones must be moved at once.

%C Both A011371 and A121924 are upper bounds for this sequence.

%H Bert Dobbelaere, <a href="/A292836/b292836.txt">Table of n, a(n) for n = 1..100</a>

%e For n = 6, two examples of a a(6) = 4 step walks to a terminal state are:

%e [1 1 1 1 1 1] -> [2, 1, 1, 1, 1] -> [2, 2, 1, 1] -> [3, 1, 1, 1] -> [3, 2, 1], and

%e [1 1 1 1 1 1] -> [2, 1, 1, 1, 1] -> [2, 2, 1, 1] -> [2, 2, 2] -> [4, 2].

%Y Cf. A011371, A121924, A292726, A292729.

%K nonn

%O 1,4

%A _Peter Kagey_, Sep 24 2017

%E a(46) onwards from _Bert Dobbelaere_, Apr 07 2024