A284689 The number of partitions of n which represent Chomp positions with Sprague-Grundy value 3.

0, 0, 0, 4, 0, 0, 4, 0, 4, 0, 6, 6, 8, 8, 8, 10, 15, 26, 17, 34, 39, 32, 73, 54, 99, 68, 133, 138, 167, 256, 261, 338, 357, 467, 545, 668, 775, 958, 1107, 1298, 1370, 1867, 2005, 2311, 2840, 3198, 3818, 4258, 4945, 5960, 6887, 8056, 9122, 10348, 12614, 14154

Offset

1,4

Comments

Chomp positions with Sprague-Grundy value 0 are the 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

Thomas J Wolf, Table of n, a(n) for n = 1..69

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.

Wikipedia, Chomp

Crossrefs

Cf. A112471, A112472, A112473.

Sequence in context: A278216 A036480 A035639 * A037214 A245198 A203285

Adjacent sequences: A284686 A284687 A284688 * A284690 A284691 A284692

Keyword

nonn

Author

Thomas J Wolf, Apr 01 2017

Status

approved