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A346705
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The a(n)-th composition in standard order is the even bisection of the n-th composition in standard order.
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2
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0, 0, 0, 1, 0, 1, 2, 1, 0, 1, 2, 1, 4, 2, 1, 3, 0, 1, 2, 1, 4, 2, 1, 3, 8, 4, 2, 5, 1, 3, 6, 3, 0, 1, 2, 1, 4, 2, 1, 3, 8, 4, 2, 5, 1, 3, 6, 3, 16, 8, 4, 9, 2, 5, 10, 5, 1, 3, 6, 3, 12, 6, 3, 7, 0, 1, 2, 1, 4, 2, 1, 3, 8, 4, 2, 5, 1, 3, 6, 3, 16, 8, 4, 9, 2, 5
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OFFSET
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0,7
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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.
a(n) is the row number in A066099 of the even bisection (even-indexed terms) of the n-th row of A066099.
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LINKS
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FORMULA
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EXAMPLE
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Composition number 741 in standard order is (2,1,1,3,2,1), with even bisection (1,3,1), which is composition number 25 in standard order, so a(741) = 25.
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MATHEMATICA
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Table[Total[2^Accumulate[Reverse[Last/@Partition[ Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse, 2]]]]/2, {n, 0, 100}]
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CROSSREFS
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Length of the a(n)-th standard composition is A000120(n)/2 rounded down.
The version for reversed prime indices appears to be A329888, sums A346700.
Sum of the a(n)-th standard composition is A346633.
An unordered reverse version for odd bisection is A346701, sums A346699.
A066099 lists compositions in standard order.
A097805 counts compositions by alternating sum.
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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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