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 A241523 The number of P-positions in the game of Nim with up to 5 piles, allowing for piles of zero, such that the number of objects in each pile does not exceed n. 5
 1, 16, 61, 256, 421, 976, 2101, 4096, 4741, 6736, 10261, 15616, 23221, 33616, 47461, 65536, 68101, 75856, 88981, 107776, 132661, 164176, 202981, 249856, 305701, 371536, 448501, 537856, 640981, 759376, 894661, 1048576, 1058821, 1089616 (list; graph; refs; listen; history; text; internal format)
 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], #[] <= a &]], {a, 0, 35}] CROSSREFS Cf. A236305 (3 piles), A241522 (4 piles). Cf. A241731 (first differences). Sequence in context: A043229 A044009 A317431 * A264632 A007831 A214524 Adjacent sequences:  A241520 A241521 A241522 * A241524 A241525 A241526 KEYWORD nonn AUTHOR Tanya Khovanova and Joshua Xiong, Apr 24 2014 STATUS approved

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Last modified August 15 18:38 EDT 2022. Contains 356148 sequences. (Running on oeis4.)