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A241718
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The number of P-positions in the game of Nim with up to 4 piles, allowing for piles of zero, such that the number of objects in the largest pile is n.
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5
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1, 7, 13, 43, 25, 79, 133, 211, 49, 151, 253, 379, 457, 607, 757, 931, 97, 295, 493, 715, 889, 1135, 1381, 1651, 1681, 1975, 2269, 2587, 2857, 3199, 3541, 3907, 193, 583, 973, 1387, 1753, 2191, 2629, 3091, 3313, 3799, 4285, 4795, 5257, 5791, 6325
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OFFSET
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0,2
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COMMENTS
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This is the first difference of A241522.
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LINKS
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FORMULA
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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) = (12*c-6)*2^b + a(c-1).
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EXAMPLE
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If the largest pile is 2, then there are 6 positions that are permutations of (0,0,2,2) plus 6 positions that are permutations of (1,1,2,2) and one position (2,2,2,2). Therefore, a(2)=13.
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MATHEMATICA
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Table[Length[Select[Flatten[Table[{n, k, j, BitXor[n, k, j]}, {n, 0, a}, {k, 0, a}, {j, 0, a}], 2], Max[#] == a &]], {a, 0, 50}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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