A364451 a(n) is the number of trees of diameter 4 with n vertices that are N-games in peg duotaire.
0, 0, 0, 0, 1, 2, 5, 7, 10, 13, 18, 22, 29, 34, 42, 49, 60, 69, 86, 100, 121, 139, 164, 187, 219, 252, 296, 343, 400, 458, 532, 605, 696, 794, 917, 1050, 1214, 1389, 1599, 1823, 2087, 2371, 2710, 3080, 3521
Offset: 1
Keywords
Examples
There is only one tree of diameter 4 with 5 vertices. It is an N-game, as evidenced by the below winning strategy for the first player. We use 1 to represent a vertex with a peg and 0 otherwise.
1-1-1-1-1
|
1-0-1-1-1
| (move is forced)
1-1-0-0-1
|
0-0-1-0-1 (no moves remain)
References
- E. R. Berlekamp, J. H. Conway, and R. K. Guy, Winning Ways for Your Mathematical Plays. Vol. 1, CRC Press, 2001.
Links
- R. A. Beeler and A. D. Gray, An Introduction to Peg Duotaire on Graphs, Journal of Combinatorial Mathematics and Combinatorial Computing, Vol. 104, 2018, pp. 171-186.
- Nathan Hurtig, SageMath program to compute values
Crossrefs
Cf. A000094.
Formula
a(n) <= A000094(n).
Comments