|
| |
|
|
A206557
|
|
Number of 7's in the last section of the set of partitions of n.
|
|
2
|
|
|
|
0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 2, 4, 5, 7, 9, 13, 16, 23, 28, 39, 48, 64, 79, 104, 128, 165, 204, 258, 317, 399, 487, 606, 739, 912, 1105, 1356, 1637, 1994, 2400, 2906, 3485, 4199, 5016, 6015, 7164, 8553, 10151, 12076, 14286, 16930, 19974, 23588, 27749
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,11
|
|
|
COMMENTS
|
Zero together with the first differences of A024791. Also number of occurrences of 7 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 seven successive terms give the partition numbers A000041.
|
|
|
LINKS
|
Table of n, a(n) for n=1..54.
|
|
|
FORMULA
|
It appears that A000041(n) = Sum_{j=1..7} a(n+j), n >= 0.
|
|
|
PROG
|
(Sage) A206557 = lambda n: sum(list(p).count(7) for p in Partitions(n) if 1 not in p)
|
|
|
CROSSREFS
|
Column 7 of A182703 and of A194812.
Cf. A000041, A135010, A138121, A182712-A182714, A206555, A206556, A206558-A206560.
Sequence in context: A094362 A000726 A128663 * A240508 A174068 A135833
Adjacent sequences: A206554 A206555 A206556 * A206558 A206559 A206560
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Omar E. Pol, Feb 09 2012
|
|
|
STATUS
|
approved
|
| |
|
|
