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A228351 Triangle read by rows in which row n lists the compositions (ordered partitions) of n (see Comments lines for definition). 13
1, 2, 1, 1, 3, 1, 2, 2, 1, 1, 1, 1, 4, 1, 3, 2, 2, 1, 1, 2, 3, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 5, 1, 4, 2, 3, 1, 1, 3, 3, 2, 1, 2, 2, 2, 1, 2, 1, 1, 1, 2, 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, 6, 1, 5, 2, 4, 1, 1, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The representation of the compositions (for fixed n) is as lists of parts, the order between individual compositions (for the same n) is (list-)reversed co-lexicographic. [Joerg Arndt, Sep 02 2013]

Dropping the "(list-)reversed" in the comment above gives A228525.

The equivalent sequence for partitions is A026792.

Row n has length A001792(n-1).

Row sums give A001787, n >= 1.

LINKS

Peter Kagey, Table of n, a(n) for n = 1..10000

EXAMPLE

Illustration of initial terms:

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

n  j     Diagram     Composition j

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

.         _

1  1     |_|         1;

.         _ _

2  1     |_  |       2,

2  2     |_|_|       1, 1;

.         _ _ _

3  1     |_    |     3,

3  2     |_|_  |     1, 2,

3  3     |_  | |     2, 1,

3  4     |_|_|_|     1, 1, 1;

.         _ _ _ _

4  1     |_      |   4,

4  2     |_|_    |   1, 3,

4  3     |_  |   |   2, 2,

4  4     |_|_|_  |   1, 1, 2,

4  5     |_    | |   3, 1,

4  6     |_|_  | |   1, 2, 1,

4  7     |_  | | |   2, 1, 1,

4  8     |_|_|_|_|   1, 1, 1, 1;

.

Triangle begins:

[1];

[2],[1,1];

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

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

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

...

PROG

(Haskell)

a228351 n = a228351_list !! (n - 1)

a228351_list = concatMap a228351_row [1..]

a228351_row 0 = []

a228351_row n = a001511 n : a228351_row (n `div` 2^(a001511 n))

-- Peter Kagey, Jun 27 2016

CROSSREFS

Cf. A001511, A006519, A011782, A026792, A065120, A066099, A228525, A228369.

Sequence in context: A128221 A175488 A115758 * A124734 A037034 A229897

Adjacent sequences:  A228348 A228349 A228350 * A228352 A228353 A228354

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Aug 30 2013

STATUS

approved

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Last modified June 20 10:13 EDT 2019. Contains 324234 sequences. (Running on oeis4.)