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A233810
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Number of starting configurations of Nim with n pieces such that 1st player wins. Partitions of n such that their xor-sum is nonzero.
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0
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0, 1, 1, 3, 3, 7, 7, 15, 16, 30, 32, 56, 61, 101, 104, 176, 188, 297, 317, 490, 529, 792, 849, 1255, 1362, 1958, 2119, 3010, 3275, 4565, 4900, 6842, 7378, 10143, 10895, 14883, 16002, 21637, 23197, 31185, 33473, 44583, 47773, 63261, 67809, 89134, 95416, 124754, 133634, 173525, 185788, 239943, 257006, 329931, 353294, 451276, 483478, 614154, 657952, 831820, 891292, 1121505, 1201037, 1505499, 1612352, 2012558, 2154724, 2679689, 2868121, 3554345, 3803081, 4697205, 5024237, 6185689, 6613581, 8118264, 8674712, 10619863, 11343319, 13848650, 14784359, 18004327
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OFFSET
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0,4
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LINKS
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FORMULA
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a(n) = Sum_{k>0} A050314(n,k). [Row sums of A050314 minus the leftmost term on each row]
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MATHEMATICA
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b[n_, i_, k_] := b[n, i, k] = If[n == 0, x^k, If[i<1, 0, Sum[b[n-i*j, i-1, If[EvenQ[j], k, BitXor[i, k]]], {j, 0, n/i}]]]; T[n_] := Function[p, Table[Coefficient[p, x, i], {i, 0, n}]][b[n, n, 0]]; a[n_] := Total[Rest[T[n]]]; Table[a[n], {n, 0, 81}] (* Jean-François Alcover, Nov 14 2016, after Alois P. Heinz *)
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CROSSREFS
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KEYWORD
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nonn,changed
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AUTHOR
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STATUS
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approved
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