A236000 - OEIS

%I #27 Apr 04 2014 13:14:04

%S 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,

%T 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,

%U 2,1,1,1,2,1,1,1,2,1,1,1,2,1,1,1,3,1,1

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

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

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

%C The equivalent sequence for partitions is A211992.

%C The equivalent sequence for compositions is A228525.

%C See both sequences for more information.

%C Row n contains A015128(n) overpartitions.

%C Row n contains A235792(n) parts.

%C Row sums give A235793.

%e Triangle begins:

%e [1], [1];

%e [1, 1], [1, 1], [2], [2];

%e [1, 1, 1], [1, 1, 1], [2, 1], [2, 1], [2, 1], [2, 1], [3], [3];

%e [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];

%e ...

%e Illustration of initial terms (n: 1..4)

%e -----------------------------------------

%e n      Diagram          Overpartition

%e -----------------------------------------

%e .       _

%e 1      |.|              1',

%e 1      |_|              1;

%e .       _ _

%e 2      |.| |            1', 1,

%e 2      |_| |            1,  1,

%e 2      |  .|            2',

%e 2      |_ _|            2;

%e .       _ _ _

%e 3      |.| | |          1', 1,  1,

%e 3      |_| | |          1,  1,  1,

%e 3      |  .|.|          2', 1',

%e 3      |   |.|          2,  1',

%e 3      |  .| |          2', 1,

%e 3      |_ _| |          2,  1,

%e 3      |    .|          3',

%e 3      |_ _ _|          3;

%e .       _ _ _ _

%e 4      |.| | | |        1', 1,  1,  1,

%e 4      |_| | | |        1,  1,  1,  1,

%e 4      |  .|.| |        2', 1', 1,

%e 4      |   |.| |        2,  1', 1,

%e 4      |  .| | |        2', 1,  1,

%e 4      |_ _| | |        2,  1,  1,

%e 4      |    .|.|        3', 1',

%e 4      |     |.|        3,  1',

%e 4      |    .| |        3', 1,

%e 4      |_ _ _| |        3,  1,

%e 4      |  .|   |        2', 2,

%e 4      |_ _|   |        2,  2,

%e 4      |      .|        4',

%e 4      |_ _ _ _|        4;

%e .

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

%K nonn,tabf

%O 1,7

%A _Omar E. Pol_, Jan 18 2014