cp's OEIS Frontend

A237711 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 is 2n.

%I A237711 #22 Mar 17 2021 07:57:42
%S A237711 1,6,7,36,13,42,43,216,49,78,55,252,85,258,259,1296,265,294,127,468,
%T A237711 133,330,307,1512,337,510,343,1548,517,1554,1555,7776,1561,1590,559,
%U A237711 1764,421,762,595,2808,601,798,463,1980,637,1842,1819,9072,1849
%N A237711 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 is 2n.
%C A237711 First differences of A237686.
%H A237711 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 A237711 a(2n+1) = 6a(n), a(2n+2) = a(n+1) + a(n).
%F A237711 G.f.: Product_{k>=0} (1 + 6*x^(2^k) + x^(2^(k+1))). - _Ilya Gutkovskiy_, Mar 16 2021
%e A237711 The P-positions with the total of 4 are permutations of (0,0,2,2) and (1,1,1,1). Therefore, a(2)=7.
%t A237711 Table[Length[
%t A237711   Select[Flatten[
%t A237711     Table[{n, k, j, BitXor[n, k, j]}, {n, 0, a}, {k, 0, a}, {j, 0,
%t A237711       a}], 2], Total[#] == a &]], {a, 0, 100, 2}]
%Y A237711 Cf. A237686 (partial sums), A048883 (3 piles), A238759 (5 piles), A241522, A241718.
%K A237711 nonn
%O A237711 0,2
%A A237711 _Tanya Khovanova_ and _Joshua Xiong_, May 02 2014