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%I #4 Mar 30 2012 17:36:54
%S 0,1,2,3,2,4,5,4,6,4,7,6,5,4,5,8,9,8,10,8,11,10,9,8,9,12,8,13,12,9,8,
%T 9,14,12,10,8,10,15,14,13,12,13,11,10,11,9,11,8,9,10,11,16,17,16,18,
%U 16,19,18,17,16,17,20,16,21,20,17,16,17,22,20,18,16,18,23,22,21,20,21,19,18
%N Consider the standard game of Nim with 3 heaps and make a list of the losing positions (x,y,z) with x <= y <= z sorted by sum, ties broken by putting smallest value of x first, then y, then z; sequence gives y values.
%C Thanks to _Ray Chandler_ for help in clarifying the relation between this sorted list and the one in A080594.
%e The triples with sum <= 20 (this sequence is the second column) are:
%e 0 0 0
%e 0 1 1
%e 0 2 2
%e 0 3 3
%e 1 2 3
%e 0 4 4
%e 0 5 5
%e 1 4 5
%e 0 6 6
%e 2 4 6
%e 0 7 7
%e 1 6 7
%e 2 5 7
%e 3 4 7
%e 3 5 6
%e 0 8 8
%e 0 9 9
%e 1 8 9
%e 0 10 10
%Y A119464, A119466 give the x and z values; A080593, A080594, A080595 give the same values sorted in a different way.
%K easy,nonn
%O 1,3
%A _Joshua Zucker_, May 21 2006
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