OFFSET
0,2
COMMENTS
P-positions in the game of Nim are tuples of numbers with a Nim-Sum equal to zero. (0,1,1,0,0) is considered different from (1,0,1,0,0).
a(2^n-1) = 2^(4n).
LINKS
T. Khovanova and J. Xiong, Nim Fractals, arXiv:1405.594291 [math.CO] (2014), p. 9 and J. Int. Seq. 17 (2014) # 14.7.8.
FORMULA
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) = 2^(4*b) + 10*2^(2*b)*c^2 + 5*c^4.
EXAMPLE
If the largest number is not more than 1, then there should be an even number of piles of size 1. We can choose the first four piles to be either 0 or 1, then the last pile is uniquely defined. Thus, a(1)=16.
MATHEMATICA
Table[Length[Select[Flatten[Table[{n, k, j, i, BitXor[n, k, j, i]}, {n, 0, a}, {k, 0, a}, {j, 0, a}, {i, 0, a}], 3], #[[5]] <= a &]], {a, 0, 35}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Tanya Khovanova and Joshua Xiong, Apr 24 2014
STATUS
approved