

A194546


Triangle read by rows: T(n,k) is the largest part of the kth partition of n, with partitions in colexicographic order.


4



1, 1, 2, 1, 2, 3, 1, 2, 3, 2, 4, 1, 2, 3, 2, 4, 3, 5, 1, 2, 3, 2, 4, 3, 5, 2, 4, 3, 6, 1, 2, 3, 2, 4, 3, 5, 2, 4, 3, 6, 3, 5, 4, 7, 1, 2, 3, 2, 4, 3, 5, 2, 4, 3, 6, 3, 5, 4, 7, 2, 4, 3, 6, 5, 4, 8, 1, 2, 3, 2, 4, 3, 5, 2, 4, 3, 6, 3, 5, 4, 7, 2, 4, 3, 6, 5, 4, 8, 3, 5, 4, 7, 3, 6, 5, 9
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


COMMENTS

Row n lists the first A000041(n) terms of A141285.
The representation of the partitions (for fixed n) is as (weakly) decreasing lists of parts, the order between individual partitions (for the same n) is colexicographic, see example.  Joerg Arndt, Sep 13 2013


LINKS

Table of n, a(n) for n=1..96.


EXAMPLE

For n = 5 the partitions of 5 in colexicographic order are:
1+1+1+1+1
2+1+1+1
3+1+1
2+2+1
4+1
3+2
5
so the fifth row is the largest in each partition: 1,2,3,2,4,3,5
Triangle begins:
1;
1,2;
1,2,3;
1,2,3,2,4;
1,2,3,2,4,3,5;
1,2,3,2,4,3,5,2,4,3,6;
1,2,3,2,4,3,5,2,4,3,6,3,5,4,7;
1,2,3,2,4,3,5,2,4,3,6,3,5,4,7,2,4,3,6,5,4,8;
...


CROSSREFS

The sum of row n is A006128(n).
Cf. A135010, A138121, A141285, A193173, A194547, A194548, A194549, A211992.
Sequence in context: A061336 A057945 A253092 * A115452 A039676 A242359
Adjacent sequences: A194543 A194544 A194545 * A194547 A194548 A194549


KEYWORD

nonn,tabf


AUTHOR

Omar E. Pol, Dec 10 2011


EXTENSIONS

Definition corrected by Omar E. Pol, Sep 12 2013


STATUS

approved



