

A316533


a(n) is the SpragueGrundy value of the NodeKayles game played on the generalized Petersen graph P(n,2).


3



1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0
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OFFSET

5


COMMENTS

For all values of n, the SpragueGrundy values of the NodeKayles game played on the generalized Petersen graph P(n,2) cannot be greater than 2 since there exist only 2 nonisomorphic first moves.
Furthermore, for all even values of n, the generalized Petersen graph P(n,2) has an automorphism defined by a rotation of 180 degrees. Hence, for every move by player 1, player 2 can respond by coloring the orbitequivalent point of player 1's move. Thus, the SpragueGrundy value of the NodeKayles game played on P(n,2) is 0 when n is even.


REFERENCES

E. R. Berlekamp, J. H. Conway, and R. K. Guy, Winning Ways for Your Mathematical Plays, Volume 1, A K Peters, 2001.


LINKS

Table of n, a(n) for n=5..26.
Sierra Brown, Spencer Daugherty, Eugene Fiorini, Barbara Maldonado, Diego ManzanoRuiz, Sean Rainville, Riley Waechter, and Tony W. H. Wong, Nimber Sequences of NodeKayles Games, J. Int. Seq., Vol. 23 (2020), Article 20.3.5.
Max Fan, Generalized NodeKayles calculator implemented in Rust
Riley S. Waechter, Python program for A316533


EXAMPLE

For n=5, a(5) is the SpragueGrundy value of the NodeKayles game played on the Petersen graph. Since the Petersen graph is vertex transitive, all first moves are isomorphic. After the first move, the resultant graph is the cycle C_6. The SpragueGrundy value of the NodeKayles game played on C_6 is 0. Hence, a(5) = mex{0} = 1, where mex is the minimum excluded function.


PROG

(Rust) // See Fan link.  Max Fan, May 23 2021


CROSSREFS

Cf. A002186, A002187 for the SpragueGrundy values of the NodeKayles games on other graphs.
Sequence in context: A171894 A284957 A357385 * A085405 A036988 A108357
Adjacent sequences: A316530 A316531 A316532 * A316534 A316535 A316536


KEYWORD

nonn,more


AUTHOR

Sierra Brown, Spencer Daugherty, Eugene Fiorini, Barbara Maldonado, Sean E. Rainville, Riley S. Waechter, Wing Hong Tony Wong, Jul 13 2018


EXTENSIONS

a(25)a(26) from Max Fan, May 23 2021


STATUS

approved



