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A194546 Triangle read by rows: T(n,k) is the largest part of the k-th 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 co-lexicographic, 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: A194436 A061336 A057945 * A115452 A039676 A113126

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

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Last modified April 19 10:50 EDT 2014. Contains 240747 sequences.