A284688 The number of partitions of n which represent Chomp positions with Sprague-Grundy value 2.

0, 0, 2, 1, 2, 0, 0, 0, 2, 2, 8, 2, 19, 0, 16, 16, 25, 14, 50, 30, 74, 64, 115, 62, 123, 120, 185, 188, 275, 318, 379, 370, 488, 550, 678, 846, 953, 1094, 1374, 1522, 1941, 2054, 2528, 3130, 3318, 4028, 4701, 5360, 6345, 7180, 8307, 9548, 11369, 12788, 14925

Offset

1,3

Comments

Chomp positions with Sprague-Grundy value 0 are losing positions. Their number is given in A112470.

References

P. M. Grundy, Mathematics and games, Eureka 2 (1939), 6-8; reprinted (1964), Eureka 27, 9-11).

Links

Table of n, a(n) for n=1..55.

Thomas S. Ferguson, Game Theory (lecture notes + exercise questions for a course on Combinatorial Game Theory).

P. M. Grundy, Mathematics and games, Eureka (The Archimedeans' Journal), No. 2, 1939, pp. 6-8. [Annotated scanned copy. My former colleague and coauthor Florence Jessie MacWilliams (nee Collinson), who was a student at Cambridge University in 1939, gave me this journal. - N. J. A. Sloane, Nov 17 2018]

R. Sprague, Über mathematische Kampfspiele, Tohoku Math. J. 41 (1936), 438-444.

R. Sprague, Über zwei Abarten von Nim, Tohoku Math. J. 43 (1937), 351-354.

Crossrefs

Cf. A112470, A112471, A112472, A112473.

Sequence in context: A322795 A050602 A065040 * A057595 A035201 A035179

Adjacent sequences: A284685 A284686 A284687 * A284689 A284690 A284691

Keyword

nonn

Author

Thomas J Wolf, Apr 01 2017

Status

approved