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A237686
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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 doesn't exceed 2n.
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5
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1, 7, 14, 50, 63, 105, 148, 364, 413, 491, 546, 798, 883, 1141, 1400, 2696, 2961, 3255, 3382, 3850, 3983, 4313, 4620, 6132, 6469, 6979, 7322, 8870, 9387, 10941, 12496, 20272, 21833, 23423, 23982, 25746, 26167, 26929, 27524, 30332, 30933
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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a(2n+1) = 7a(n) + a(n-1), a(2n+2) = a(n+1) + 7a(n).
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EXAMPLE
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There is a position (0,0,0,0) with a total of zero. There are 6 positions with a total of 2 that are permutations of (0,0,1,1). Therefore, a(1)=7.
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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], Total[#] <= a &]], {a, 0, 100, 2}]
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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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