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A119464

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.

+0
6

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, 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, 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 (list; graph; listen)

	OFFSET	`1,10`
	COMMENT	`Thanks to Ray Chandler (rayjchandler(AT)sbcglobal.net) for help in clarifying the relation between this sorted list and the one in A080593.`
	EXAMPLE	`The triples with sum <= 20 (this sequence is the first column) are:` `0 0 0` `0 1 1` `0 2 2` `0 3 3` `1 2 3` `0 4 4` `0 5 5` `1 4 5` `0 6 6` `2 4 6` `0 7 7` `1 6 7` `2 5 7` `3 4 7` `3 5 6` `0 8 8` `0 9 9` `1 8 9` `0 10 10`
	CROSSREFS	`Cf. A119465, A119466 give the y and z values; A080593, A080594, A080595 give the same values sorted in a different way.` `Sequence in context: A079686 A005813 A049262 this_sequence A107017 A049260 A053186` `Adjacent sequences: A119461 A119462 A119463 this_sequence A119465 A119466 A119467`
	KEYWORD	`easy,nonn`
	AUTHOR	`Joshua Zucker (joshua.zucker(AT)stanfordalumni.org), May 21 2006`

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Last modified August 29 17:54 EDT 2008. Contains 143238 sequences.

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