|
|
A229898
|
|
Number of c-squarefree numbers (A233564) less than 2^n.
|
|
0
|
|
|
0, 1, 2, 5, 8, 13, 24, 37, 56, 83, 140, 205, 306, 439, 632, 983, 1418, 2035, 2886, 4063, 5618, 8369, 11666, 16423, 22716, 31477, 42782, 58385, 82700, 113161, 155028, 210769, 285644, 383687, 514496, 682921, 940326, 1256299, 1687364, 2245691, 2997182, 3955447, 5233314
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
For n >= 1, a(n) is the total number of compositions of positive integers less than or equal to n with distinct parts (cf. A032020).
For example, numbers of such compositions of 1,2,3,4,5 are 1,1,3,3,5. So a(5)=13.
|
|
LINKS
|
|
|
FORMULA
|
G.f.: (1/(1 - x)) * Sum_{i>=1} i!*x^(i*(i+1)/2) * Product_{j=1..i} 1/(1 - x^j). - Ilya Gutkovskiy, Apr 04 2017
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|