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

1, 4, 22, 1474

Offset

0,2

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 and the upper bound of 10^434 for a(4). - Christopher E. Thompson, Aug 06 2015

Koki Suetsugu improved the lower and upper bounds of a(4), and the lower bound is 10^28.2, and the upper bound is 4*10^184. - Zhujun Zhang, May 06 2026

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

Table of n, a(n) for n=0..3.

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

Koki Suetsugu, Improving upper and lower bounds of the number of games born by day 4, arXiv:2208.13403 [math.CO], 2022-2024; pp. 447-460 in Games of No Chance 6, edited by U. Larsson, Math. Sci. Res. Inst. Publ. 71, Cambridge Univ. Press, 2025.

Formula

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

Crossrefs

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

Sequence in context: A362823 A368140 A273054 * A053775 A037142 A115989

Adjacent sequences: A065398 A065399 A065400 * A065402 A065403 A065404

Keyword

nonn,hard,more,changed

Author

R. K. Guy, Nov 23 2001

Extensions

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

Status

approved