A263453 Number of starting positions of Kayles with n pieces such that the 2nd player can win (P-positions).

1, 0, 1, 0, 2, 1, 4, 1, 6, 7, 9, 9, 17, 17, 30, 25, 44, 49, 74, 67, 109, 125, 164, 188, 245, 285, 390, 424, 551, 645, 847, 933, 1199, 1393, 1747, 2047, 2463, 2893, 3622, 4161, 5016, 5863, 7203, 8282, 9973, 11533, 13927, 16300, 19095, 22213, 26645, 30823, 36166

Offset: 0

Author

Brian Hopkins, Oct 18 2015

Keywords

• nonn

Comments

The partition p = (p_1,...,p_k) is counted if the Nimsum of the A002186(p_i) is 0.

Examples

			For n = 6 the a(6) = 4 P-positions are (3,3), (3,2,1), (2,2,1,1), and (1,1,1,1,1,1).
		

Links

• Eric M. Schmidt, Table of n, a(n) for n = 0..10000
• Eric M. Schmidt, C++ code to compute this sequence
• Wikipedia, Kayles

Crossrefs

Cf. A002186, A048833, A263454.

Extensions

a(0) and more terms from Eric M. Schmidt, Jan 11 2017