A206557 Number of 7's in the last section of the set of partitions of n.

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

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