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The number of partitions of n which represent Chomp positions with Sprague-Grundy value 2.
1

%I #22 Dec 19 2022 09:42:42

%S 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,

%T 185,188,275,318,379,370,488,550,678,846,953,1094,1374,1522,1941,2054,

%U 2528,3130,3318,4028,4701,5360,6345,7180,8307,9548,11369,12788,14925

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

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

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

%H Thomas S. Ferguson, <a href="https://www.mina.moe/wp-content/uploads/2018/05/GAME-THEORY-Thomas-S.Ferguson.pdf">Game Theory</a> (lecture notes + exercise questions for a course on Combinatorial Game Theory).

%H P. M. Grundy, <a href="/A002188/a002188.pdf">Mathematics and games</a>, 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]

%H R. Sprague, <a href="https://www.jstage.jst.go.jp/article/tmj1911/41/0/41_0_438/_article">Über mathematische Kampfspiele</a>, Tohoku Math. J. 41 (1936), 438-444.

%H R. Sprague, <a href="https://www.jstage.jst.go.jp/article/tmj1911/43/0/43_0_351/_article">Über zwei Abarten von Nim</a>, Tohoku Math. J. 43 (1937), 351-354.

%Y Cf. A112470, A112471, A112472, A112473.

%K nonn

%O 1,3

%A _Thomas J Wolf_, Apr 01 2017