A145573 Characteristic partition array for partitions without part 1.

0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0

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.

The row lengths of this array are p(n)=A000041(n) (number of partitions of n).

The entries of row n are grouped together for 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 A145574.

Links

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

W. Lang and M. Sjodahl First 10 rows of the array and row sums.

Formula

As array: a(n,k)=1 if the k-th partition of n in A-St order has no part 1, 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

[0],[1,0],[1,0,0],[1,0,1,0,0],[1,0,1,0,0,0,0],...
a(4,3) = a(1+2+3+3) = a(9) = 1 because a(4,3) belongs to the partition [2^2]=[2,2] of n=4 which has no part 1.

Crossrefs

Cf. A145574 (without zeros). A002865 (row sums).

Sequence in context: A215530 A241422 A189661 * A092202 A358846 A285686

Adjacent sequences: A145570 A145571 A145572 * A145574 A145575 A145576

Keyword

nonn,easy,tabf

Author

Wolfdieter Lang and Malin Sjodahl, Mar 06 2009

Status

approved