%I #4 Mar 30 2012 17:36:54
%S 0,0,0,0,1,0,0,1,0,2,0,1,2,3,3,0,0,1,0,2,0,1,2,3,3,0,4,0,1,4,5,5,0,2,
%T 4,6,6,0,1,2,3,3,4,5,5,6,6,7,7,7,7,0,0,1,0,2,0,1,2,3,3,0,4,0,1,4,5,5,
%U 0,2,4,6,6,0,1,2,3,3,4,5,5,6,6,7,7,7,7,0,8,0,1,8,9,9,0,2,8,10,10,0,1,2,3,3
%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 x values.
%C Thanks to _Ray Chandler_ for help in clarifying the relation between this sorted list and the one in A080593.
%e The triples with sum <= 20 (this sequence is the first 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 Cf. A119465, A119466 give the y and z values; A080593, A080594, A080595 give the same values sorted in a different way.
%K easy,nonn
%O 1,10
%A _Joshua Zucker_, May 21 2006