|
Search: id:A117146
|
|
|
| A117146 |
|
Number of parts in all s-partitions of n. An s-partition of n is a partition of n into parts of the form 2^j-1 (j=1,2,...). |
|
+0
2
|
|
| 1, 2, 4, 6, 8, 12, 16, 20, 27, 34, 40, 50, 60, 70, 85, 100, 115, 136, 156, 176, 206, 234, 261, 300, 336, 370, 418, 466, 511, 572, 633, 690, 765, 840, 914, 1008, 1102, 1194, 1307, 1420, 1530, 1668, 1806, 1940, 2107, 2272, 2431, 2626, 2825, 3016, 3246, 3484
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
a(n)=sum(k*A117145(n,k), k=1..n).
|
|
REFERENCES
|
P. C. P. Bhatt, An interesting way to partition a number, Inform. Process. Lett., 71, 1999, 141-148.
W. M. Y. Goh, P. Hitczenko and A. Shokoufandeh, s-partitions, Inform. Process. Lett., 82, 2002, 327-329.
|
|
FORMULA
|
G.f.=sum(x^(2^k-1)/(1-x^(2^k-1)), k=1..infinity)/product(1-x^(2^k-1), k=1..infinity).
|
|
EXAMPLE
|
a(7)=16 because the s-partitions of 7 are [7],[3,3,1],[3,1,1,1,1], and [1,1,1,1,1,1,1], with a total of 1+3+5+7=16 parts.
|
|
MAPLE
|
g:=sum(x^(2^k-1)/(1-x^(2^k-1)), k=1..10)/product(1-x^(2^k-1), k=1..10): gser:=series(g, x=0, 60): seq(coeff(gser, x^n), n=1..56);
|
|
CROSSREFS
|
Cf. A117145.
Sequence in context: A064522 A036912 A097921 this_sequence A061553 A138934 A008764
Adjacent sequences: A117143 A117144 A117145 this_sequence A117147 A117148 A117149
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 06 2006
|
|
|
Search completed in 0.002 seconds
|
