A364489 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

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.

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

(list; graph; refs; listen; history; text; internal format)

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.

LINKS

Table of n, a(n) for n=1..43.

Nathan Hurtig, C++ program to compute values

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.