A065401 Number of normal play partisan games born on or before day n.

1, 4, 22, 1474

Offset: 0

Author

R. K. Guy, Nov 23 2001

Keywords

• nonn
• hard
• more

Comments

Fraser and Wolfe prove upper and lower bounds on a(n+1) in terms of a(n). In particular they give the (probably quite weak) lower bound of 3*10^12 for a(4). - Christopher E. Thompson, Aug 06 2015

References

• Dan Calistrate, Marc Paulhus and David Wolfe, On the lattice structure of finite games, in More Games of No Chance (Berkeley, CA, 2000), Math. Sci. Res. Inst. Publ., 42, Cambridge Univ. Press, Cambridge, 2002, pp. 25-30.
• J. H. Conway, On Numbers and Games, Academic Press, NY, 1976.
• Aaron N. Siegel, Combinatorial Game Theory, AMS Graduate Texts in Mathematics Vol 146 (2013), p. 158.

Links

• William E. Fraser and David Wolfe, Counting the number of games, Theoret. Comput. Sci. 313 (2004), pp. 527-532.

Crossrefs

Cf. A065402, A065407, A047995, A037142, A114561, A125990, A126011.

Formula

a(n) = A125990(2*A114561(n)). - Antti Karttunen, Oct 18 2018

Extensions

Dean Hickerson and Robert Li found a(3) in 1974.