|
|
A206558
|
|
Number of 8's in the last section of the set of partitions of n.
|
|
3
|
|
|
0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 2, 4, 4, 8, 8, 13, 15, 23, 26, 38, 45, 63, 74, 101, 120, 160, 191, 248, 298, 383, 457, 579, 694, 868, 1038, 1287, 1536, 1890, 2251, 2746, 3267, 3962, 4698, 5665, 6706, 8043, 9496, 11337, 13354, 15876, 18657, 22089
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,12
|
|
COMMENTS
|
Zero together with the first differences of A024792. Also number of occurrences of 8 in all partitions of n that do not contain 1 as a part. For the definition of "last section of n" see A135010. It appears that the sums of eight successive terms give the partition numbers A000041.
|
|
LINKS
|
|
|
FORMULA
|
It appears that A000041(n) = Sum_{j=1..8} a(n+j), n >= 0.
|
|
PROG
|
(Sage) A206558 = lambda n: sum(list(p).count(8) for p in Partitions(n) if 1 not in p)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|