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A364489
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Values of n for which the Sprague-Grundy value of Heat-Charge Toggle on an (n+2)-vertex path with initial weights -1,1^n,-1 is evil for odd n or odious for even n.
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2
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1, 4, 6, 9, 14, 22, 27, 30, 35, 41, 58, 59, 72, 84, 87, 89, 103, 105, 108, 124, 129, 141, 171, 258, 284, 407, 458, 11770548, 25146268, 27690032, 41693544, 55788270, 74838555, 86120064, 89811321, 95580294, 119784327, 139336981, 158776090, 160066751, 161102638, 181691114, 186919128
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OFFSET
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1,2
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COMMENTS
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Heat-Charge Toggle is an impartial two-player game on a finite simple graph, where each vertex is assigned a weight of -1, 0, or 1.
A Heat-Charge Toggle move consists of selecting a vertex of weight 1 and switching its weight to 0, as well as switching the sign of each of its neighbors: changing 1 to -1, -1 to 1, and keeping 0 at 0.
We additionally only allow moves that strictly decrease the sum of all weights.
The two vertices of degree one have initial weights of -1, while vertices of degree two have an initial weight of 1.
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REFERENCES
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E. R. Berlekamp, J. H. Conway, and R. K. Guy, Winning Ways for Your Mathematical Plays, Vol. 1, CRC Press, 2001.
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LINKS
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EXAMPLE
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For n = 4, the Sprague-Grundy value for a 6-vertex path is 2.
Note that n = 4 is even and 2 is odious (see A000069).
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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