

A241523


The number of Ppositions 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
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OFFSET

0,2


COMMENTS

Ppositions in the game of Nim are tuples of numbers with a NimSum equal to zero. (0,1,1,0,0) is considered different from (1,0,1,0,0).
a(2^n1) = 2^(4n).


LINKS



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



STATUS

approved



