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A358525
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Number of distinct permutations of the n-th composition in standard order.
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0
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1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 3, 2, 3, 3, 1, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 1, 1, 2, 2, 3, 1, 6, 6, 4, 2, 6, 1, 6, 6, 6, 6, 5, 2, 3, 6, 4, 6, 6, 6, 5, 3, 4, 6, 5, 4, 5, 5, 1, 1, 2, 2, 3, 2, 6, 6, 4, 2, 3, 3, 12, 3, 12, 12, 5, 2, 6, 3, 12, 3, 4
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OFFSET
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0,6
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COMMENTS
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The k-th composition in standard order (graded reverse-lexicographic, A066099) is obtained by taking the set of positions of 1's in the reversed binary expansion of k, prepending 0, taking first differences, and reversing again. This gives a bijective correspondence between nonnegative integers and integer compositions.
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LINKS
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EXAMPLE
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The a(45) = 6 permutations are: (2121), (2112), (2211), (1221), (1212), (1122).
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MATHEMATICA
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stc[n_]:=Reverse[Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n, 2]], 1], 0]]];
Table[Length[Permutations[stc[n]]], {n, 0, 100}]
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CROSSREFS
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See link for sequences related to standard compositions.
Cf. A000120, A048896, A070939, A329395, A333766, A358371, A358372, A358379, A358505, A358507, A358508.
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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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