%I
%S 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,
%T 285,390,424,551,645,847,933,1199,1393,1747,2047,2463,2893,3622,4161,
%U 5016,5863,7203,8282,9973,11533,13927,16300,19095,22213,26645,30823,36166
%N Number of starting positions of Kayles with n pieces such that the 2nd player can win (Ppositions).
%C The partition p = (p_1,...,p_k) is counted if the Nimsum of the A002186(p_i) is 0.
%H Eric M. Schmidt, <a href="/A263453/b263453.txt">Table of n, a(n) for n = 0..10000</a>
%H Eric M. Schmidt, <a href="/A263453/a263453.cpp.txt">C++ code to compute this sequence</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Kayles">Kayles</a>
%e For n = 6 the a(6) = 4 Ppositions are (3,3), (3,2,1), (2,2,1,1), and (1,1,1,1,1,1).
%Y Cf. A002186, A048833, A263454.
%K nonn
%O 0,5
%A _Brian Hopkins_, Oct 18 2015
%E a(0) and more terms from _Eric M. Schmidt_, Jan 11 2017
