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A145573 Characteristic partition array for partitions without part 1. 3
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 (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.

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, 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 A285686 A303591

Adjacent sequences:  A145570 A145571 A145572 * A145574 A145575 A145576

KEYWORD

nonn,easy,tabf

AUTHOR

Wolfdieter Lang and Malin Sjodahl, Mar 06 2009

STATUS

approved

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Last modified August 20 03:33 EDT 2019. Contains 326139 sequences. (Running on oeis4.)