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A238147
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The number of P-positions in the game of Nim with up to five piles, allowing for piles of zero, such that the total number of objects in all piles doesn't exceed 2n.
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2
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1, 11, 26, 126, 191, 341, 516, 1516, 2081, 2731, 3206, 4706, 5631, 7381, 9256, 19256, 24821, 30471, 33946, 40446, 44171, 48921, 52796, 67796, 76221, 85471, 91846, 109346, 119971, 138721, 158096, 258096, 313661, 369311
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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) = 11a(n) + 5a(n-1), a(2n+2) = a(n+1) + 15a(n).
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EXAMPLE
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There is 1 position (0,0,0,0,0) with a total of zero. There are 10 positions with a total of 2 that are permutations of (0,0,0,1,1). Therefore, a(1)=11.
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MATHEMATICA
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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}]
(* Second program: *)
a[n_] := a[n] = Which[n <= 1, {1, 11}[[n+1]], OddQ[n], 11 a[(n-1)/2] + 5 a[(n-1)/2 - 1], EvenQ[n], a[(n-2)/2 + 1] + 15*a[(n-2)/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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