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A228528 Triangle read by rows in which row n lists the compositions (ordered partitions) of n (see Comments lines for definition). 0
1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 2, 3, 3, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 3, 4, 4, 1, 1, 3, 1, 2, 2, 1, 1, 1, 2, 1, 3, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 2, 2, 3, 2, 1, 1, 3, 2, 3, 1, 4, 5, 5, 1, 1, 4, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

In order to construct this sequence we use the following rules: T(1,1) = 1. For n >= 2, row n lists the last 2^(n-2) compositions from the n-th row of triangle A228351 and then the last 2^(n-2) compositions from the n-th row of triangle A228525. In both cases these compositions are listed in the same order as they are listed in the mentioned triangles.

Row n has length A001792(n-1).

Row sums give A001787, n >= 1.

First differs from A227736 at a(18).

LINKS

Table of n, a(n) for n=1..85.

EXAMPLE

Illustration of initial terms:

---------------------------------------

n   j     Diagram        Composition j

---------------------------------------

.          _

1   1     |_|_           1;

2   1     |_| |          1, 1,

2   2     |_ _|_         2;

3   1     |_  | |        2, 1,

3   2     |_|_| |        1, 1, 1,

3   3     |_|   |        1, 2,

3   4     |_ _ _|_       3;

4   1     |_    | |      3, 1,

4   2     |_|_  | |      1, 2, 1,

4   3     |_  | | |      2, 1, 1,

4   4     |_|_|_| |      1, 1, 1, 1,

4   5     |_| |   |      1, 1, 2,

4   6     |_ _|   |      2, 2,

4   7     |_|     |      1, 3,

4   8     |_ _ _ _|_     4;

5   1     |_      | |    4, 1,

5   2     |_|_    | |    1, 3, 1,

5   3     |_  |   | |    2, 2, 1,

5   4     |_|_|_  | |    1, 1, 2, 1,

5   5     |_    | | |    3, 1, 1,

5   6     |_|_  | | |    1, 2, 1, 1,

5   7     |_  | | | |    2, 1, 1, 1,

5   8     |_|_|_|_| |    1, 1, 1, 1, 1,

5   9     |_| | |   |    1, 1, 1, 2,

5  10     |_ _| |   |    2, 1, 2,

5  11     |_|   |   |    1, 2, 2,

5  12     |_ _ _|   |    3, 2,

5  13     |_| |     |    1, 1, 3,

5  14     |_ _|     |    2, 3,

5  15     |_|       |    1, 4,

5  16     |_ _ _ _ _|    5;

.

Triangle begins:

[1];

[1,1], [2];

[2,1], [1,1,1], [1,2], [3];

[3,1], [1,2,1], [2,1,1], [1,1,1,1], [1,1,2], [2,2], [1,3], [4];

[4,1], [1,3,1], [2,2,1], [1,1,2,1], [3,1,1], [1,2,1,1], [2,1,1,1], [1,1,1,1,1], [1,1,1,2], [2,1,2], [1,2,2], [3,2], [1,1,3], [2,3], [1,4], [5];

CROSSREFS

Cf. A001792, A001787, A011782, A066099, A227736, A228525, A228351, A228369.

Sequence in context: A300751 A070000 A227736 * A219244 A323017 A273638

Adjacent sequences:  A228525 A228526 A228527 * A228529 A228530 A228531

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Sep 07 2013

STATUS

approved

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Last modified July 16 04:26 EDT 2019. Contains 325064 sequences. (Running on oeis4.)