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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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
| W. Lang First 10 rows of the array.
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FORMULA
| 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
| [1];[1,0];[1,1,0];[1,1,0,0,0];[1,1,1,0,0,0,0];...
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CROSSREFS
| Cf. A000009 (row sums).
Sequence in context: A114986 A014282 A014555 * A077605 A014672 A015335
Adjacent sequences: A145572 A145573 A145574 * A145576 A145577 A145578
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KEYWORD
| nonn,easy,tabf
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AUTHOR
| A145575 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Mar 06 2009
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