

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 AbramowitzStegun (ASt order). See e.g. A036040 for the reference, pp. 8312.
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 kth partition of n in ASt 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



