A236000 Triangle read by rows in which row n lists the overpartitions of n in colexicographic order.

1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 3, 1, 3, 1, 3, 1, 3, 1, 2, 2, 2, 2, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1

Offset

1,7

Comments

In the data section the overlined parts cannot be represented correctly, therefore the sequence represents all possible suborderings generated by the overlined parts.

The diagram in the second part of the Example section shows only one of the possible suborderings.

The equivalent sequence for partitions is A211992.

The equivalent sequence for compositions is A228525.

See both sequences for more information.

Row n contains A015128(n) overpartitions.

Row n contains A235792(n) parts.

Row sums give A235793.

Links

Table of n, a(n) for n=1..87.

Example

Triangle begins:
[1], [1];
[1, 1], [1, 1], [2], [2];
[1, 1, 1], [1, 1, 1], [2, 1], [2, 1], [2, 1], [2, 1], [3], [3];
[1, 1, 1, 1], [1, 1, 1, 1], [2, 1, 1], [2, 1, 1], [2, 1, 1], [2, 1, 1], [3, 1], [3, 1], [3, 1], [3, 1], [2, 2], [2, 2], [4], [4];
...
Illustration of initial terms (n: 1..4)
-----------------------------------------
n      Diagram          Overpartition
-----------------------------------------
.       _
1      |.|              1',
1      |_|              1;
.       _ _
2      |.| |            1', 1,
2      |_| |            1,  1,
2      |  .|            2',
2      |_ _|            2;
.       _ _ _
3      |.| | |          1', 1,  1,
3      |_| | |          1,  1,  1,
3      |  .|.|          2', 1',
3      |   |.|          2,  1',
3      |  .| |          2', 1,
3      |_ _| |          2,  1,
3      |    .|          3',
3      |_ _ _|          3;
.       _ _ _ _
4      |.| | | |        1', 1,  1,  1,
4      |_| | | |        1,  1,  1,  1,
4      |  .|.| |        2', 1', 1,
4      |   |.| |        2,  1', 1,
4      |  .| | |        2', 1,  1,
4      |_ _| | |        2,  1,  1,
4      |    .|.|        3', 1',
4      |     |.|        3,  1',
4      |    .| |        3', 1,
4      |_ _ _| |        3,  1,
4      |  .|   |        2', 2,
4      |_ _|   |        2,  2,
4      |      .|        4',
4      |_ _ _ _|        4;
.

Crossrefs

Cf. A015128, A211992, A228525, A235790, A235792, A235793, A235797, A235798, A236001

Sequence in context: A094215 A329040 A296978 * A114139 A195679 A029884

Adjacent sequences: A235997 A235998 A235999 * A236001 A236002 A236003

Keyword

nonn,tabf

Author

Omar E. Pol, Jan 18 2014

Status

approved