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A228720
Number of partitions in the first n compositions of j, according with the ordering of A228525, if 1<=n<=2^(j-1).
3
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.
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.
Sequence in context: A035100 A303594 A085089 * A219652 A069924 A377028
KEYWORD
nonn
AUTHOR
Omar E. Pol, Aug 30 2013
STATUS
approved