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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 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=1..105.

Wolfdieter Lang, First 10 rows of the array.

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: A188017 A286755 A286349 * A077605 A323512 A014672

Adjacent sequences:  A145572 A145573 A145574 * A145576 A145577 A145578

KEYWORD

nonn,easy,tabf

AUTHOR

Wolfdieter Lang, Mar 06 2009

STATUS

approved

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Last modified July 17 14:44 EDT 2019. Contains 325106 sequences. (Running on oeis4.)