|
Search: id:A129921
|
|
|
| A129921 |
|
Number of generalized compositions of n, i.e. words b_1^{i_1}b_2^{i_2}...b_k^{i_k} such that b_j's and j_i's are positive integers and sum b_j*i_j=n. |
|
+0
1
|
|
| 1, 1, 3, 7, 18, 43, 108, 263, 651, 1599, 3942, 9698, 23890, 58805, 144806, 356512, 877820, 2161285, 5321485, 13102246, 32259890
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
Under the additional assumption that b_j does not equal to b_{j+1} the sequence enumerates the compositions (ordered partitions) of integers.
|
|
REFERENCES
|
S. Corteel, P. Hitczenko, Generalizations of Carlitz compositions, preprint
|
|
FORMULA
|
generating function = 1/(1-sum( k>0 z^k/(1-z^k))
|
|
EXAMPLE
|
a(3)=7 because we can write 3^{1}, 1^{2}2^{1}, 2^{1}1^{1}, 1^{3}, 1^{2}1^{1}, 1^{1}1^{2}, 1^{1}1^{1}1^{1}
|
|
CROSSREFS
|
Cf. A000079.
Sequence in context: A000633 A036669 A091621 this_sequence A036670 A027967 A000226
Adjacent sequences: A129918 A129919 A129920 this_sequence A129922 A129923 A129924
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
pawel hitczenko (phitczenko(AT)math.drexel.edu), Jun 05 2007
|
|
|
Search completed in 0.002 seconds
|
