cp's OEIS Frontend

A237686 The number of P-positions in the game of Nim with up to four piles, allowing for piles of zero, such that the total number of objects in all piles doesn't exceed 2n.

%I A237686 #25 Feb 28 2018 15:07:44
%S A237686 1,7,14,50,63,105,148,364,413,491,546,798,883,1141,1400,2696,2961,
%T A237686 3255,3382,3850,3983,4313,4620,6132,6469,6979,7322,8870,9387,10941,
%U A237686 12496,20272,21833,23423,23982,25746,26167,26929,27524,30332,30933
%N A237686 The number of P-positions in the game of Nim with up to four piles, allowing for piles of zero, such that the total number of objects in all piles doesn't exceed 2n.
%C A237686 Partial sums of A237711.
%H A237686 T. Khovanova and J. Xiong, <a href="http://arxiv.org/abs/1405.5942">Nim Fractals</a>, arXiv:1405.594291 [math.CO] (2014), p. 16 and <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Khovanova/khova6.html">J. Int. Seq. 17 (2014) # 14.7.8</a>.
%F A237686 a(2n+1) = 7a(n) + a(n-1), a(2n+2) = a(n+1) + 7a(n).
%e A237686 There is a position (0,0,0,0) with a total of zero. There are 6 positions with a total of 2 that are permutations of (0,0,1,1). Therefore, a(1)=7.
%t A237686 Table[Length[
%t A237686   Select[Flatten[
%t A237686     Table[{n, k, j, BitXor[n, k, j]}, {n, 0, a}, {k, 0, a}, {j, 0,
%t A237686       a}], 2], Total[#] <= a &]], {a, 0, 100, 2}]
%Y A237686 Cf. A237711 (first differences), A130665 (3 piles), A238147 (5 piles), A241522, A241718.
%K A237686 nonn
%O A237686 0,2
%A A237686 _Tanya Khovanova_ and _Joshua Xiong_, May 02 2014