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%I #21 Feb 28 2018 15:05:11
%S 1,7,13,43,25,79,133,211,49,151,253,379,457,607,757,931,97,295,493,
%T 715,889,1135,1381,1651,1681,1975,2269,2587,2857,3199,3541,3907,193,
%U 583,973,1387,1753,2191,2629,3091,3313,3799,4285,4795,5257,5791,6325
%N The number of P-positions in the game of Nim with up to 4 piles, allowing for piles of zero, such that the number of objects in the largest pile is n.
%C This is the first difference of A241522.
%H T. Khovanova and J. Xiong, <a href="http://arxiv.org/abs/1405.5942">Nim Fractals</a>, arXiv:1405.594291 [math.CO], 2014, p. 8 and <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Khovanova/khova6.html">J. Int. Seq. 17 (2014) # 14.7.8</a>.
%F If b = floor(log_2(n)) is the number of digits in the binary representation of n and c = n + 1 - 2^b, then a(n) = (12*c-6)*2^b + a(c-1).
%e If the largest pile is 2, then there are 6 positions that are permutations of (0,0,2,2) plus 6 positions that are permutations of (1,1,2,2) and one position (2,2,2,2). Therefore, a(2)=13.
%t Table[Length[Select[Flatten[Table[{n, k, j, BitXor[n, k, j]}, {n, 0, a}, {k, 0, a}, {j, 0, a}], 2], Max[#] == a &]], {a, 0, 50}]
%Y Cf. A241522, A241717 (3 piles), A241731 (5 piles).
%K nonn
%O 0,2
%A _Tanya Khovanova_ and _Joshua Xiong_, Apr 27 2014
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