A228720 Number of partitions in the first n compositions of j, according with the ordering of A228525, if 1<=n<=2^(j-1).

1, 2, 2, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15

Offset

1,2

Comments

For a program, see A228525.

Links

Table of n, a(n) for n=1..70.

Formula

a(2^(n-1)) = A000041(n), n >= 1.

Example

For n = 13 there are only six partitions in the first 13 rows of the list of compositions of any integer >= 5, so a(13) = 6.
---------------------------------------------------------
.               |          Compositions of j
.               |
n  a(n) A228354 | 1    2     3       4         5
---------------------------------------------------------
.
1   1  *   1      1    1+1   1+1+1   1+1+1+1   1+1+1+1+1
2   2  *   2           2     2+1     2+1+1     2+1+1+1
3   2                        1+2     1+2+1     1+2+1+1
4   3  *   4                 3       3+1       3+1+1
5   3                                1+1+2     1+1+2+1
6   4  *   6                         2+2       2+2+1
7   4                                1+3       1+3+1
8   5  *   8                         4         4+1
9   5                                          1+1+1+2
10  5                                          2+1+2
11  5                                          1+2+2
12  6  *  12                                   3+2
13  6                                          1+1+3
14  6                                          2+3
15  6                                          1+4
16  7  *  16                                   5
...

Crossrefs

Where records occur here are in A228354.

Cf. A000041, A011782, A211992, A228525.

Sequence in context: A035100 A303594 A085089 * A219652 A069924 A225559

Adjacent sequences: A228717 A228718 A228719 * A228721 A228722 A228723

Keyword

nonn

Author

Omar E. Pol, Aug 30 2013

Status

approved