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%I #4 Mar 30 2012 17:36:54
%S 0,1,2,3,3,4,5,5,6,6,7,7,7,7,6,8,9,9,10,10,11,11,11,11,10,12,12,13,13,
%T 13,13,12,14,14,14,14,12,15,15,15,15,14,15,15,14,15,13,15,14,13,12,16,
%U 17,17,18,18,19,19,19,19,18,20,20,21,21,21,21,20,22,22,22,22,20,23,23
%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 z values.
%C Thanks to _Ray Chandler_ for help in clarifying the relation between this sorted list and the one in A080595.
%e The triples with sum <= 20 (this sequence is the third
%e 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, A119465 give the x and y 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