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A145575
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Characteristic partition array for partitions with distinct parts.
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1
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1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1
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OFFSET
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1,1
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COMMENTS
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The partitions are ordered according to Abramowitz-Stegun (A-St order). See e.g. A036040 for the reference, pp. 831-2.
Partitions with distinct parts could be called fermionic partitions, because the places 1,...,n for the possible parts are either empty or once occupied.
The row lengths of this array are p(n)=A000041(n) (number of partitions of n).
The entries of row n belong to partitions with rising parts number m from 1 to n. The number of partitions of n with m parts is p(n,m)= A008284(n,m), m=1..n, n>=1.
For the array without zeros see A008289.
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LINKS
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FORMULA
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As array: a(n,k)=1 if the k-th partition of n in A-St order has distinct parts, and a(n,k)=0 else.
Translated into the sequence a(m) entry: a(n,k) = a(sum(p(k),k=1..n)+k).
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EXAMPLE
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[1];[1,0];[1,1,0];[1,1,0,0,0];[1,1,1,0,0,0,0];...
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CROSSREFS
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KEYWORD
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nonn,easy,tabf
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AUTHOR
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STATUS
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approved
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