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A145575
Characteristic partition array for partitions with distinct parts.
1
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
OFFSET
1,1
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.
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).
EXAMPLE
[1];[1,0];[1,1,0];[1,1,0,0,0];[1,1,1,0,0,0,0];...
CROSSREFS
Cf. A000009 (row sums).
Sequence in context: A371931 A286755 A286349 * A077605 A323512 A014672
KEYWORD
nonn,easy,tabf
AUTHOR
Wolfdieter Lang, Mar 06 2009
STATUS
approved