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%I #15 Sep 03 2023 11:17:28
%S 1,4,6,9,14,22,27,30,35,41,58,59,72,84,87,89,103,105,108,124,129,141,
%T 171,258,284,407,458,11770548,25146268,27690032,41693544,55788270,
%U 74838555,86120064,89811321,95580294,119784327,139336981,158776090,160066751,161102638,181691114,186919128
%N 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.
%C 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.
%C 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.
%C We additionally only allow moves that strictly decrease the sum of all weights.
%C The two vertices of degree one have initial weights of -1, while vertices of degree two have an initial weight of 1.
%D E. R. Berlekamp, J. H. Conway, and R. K. Guy, Winning Ways for Your Mathematical Plays, Vol. 1, CRC Press, 2001.
%H Nathan Hurtig, <a href="/A364489/a364489.cpp.txt">C++ program to compute values</a>
%e For n = 4, the Sprague-Grundy value for a 6-vertex path is 2.
%e Note that n = 4 is even and 2 is odious (see A000069).
%Y Cf. A000069, A001969, A361517, A363934. Paths with Sprague-Grundy values A364503.
%K nonn
%O 1,2
%A _Jean-Pierre Appel_, _Patrick G. Cesarz_, _Djeneba Diop_, _Eugene Fiorini_, _Nathan Hurtig_, _Andrew Woldar_, Jul 26 2023