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A364489
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.
2
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
OFFSET
1,2
COMMENTS
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.
REFERENCES
E. R. Berlekamp, J. H. Conway, and R. K. Guy, Winning Ways for Your Mathematical Plays, Vol. 1, CRC Press, 2001.
EXAMPLE
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).
CROSSREFS
Cf. A000069, A001969, A361517, A363934. Paths with Sprague-Grundy values A364503.
Sequence in context: A073679 A257559 A118689 * A118692 A020706 A226271
KEYWORD
nonn
STATUS
approved