A286755 Möbius (or Moebius) partition function of partitions in graded reverse lexicographic ordering.

-1, -1, 0, -1, 1, 0, -1, 1, 0, 0, 0, -1, 1, 1, 0, 0, 0, 0, -1, 1, 1, 0, 0, -1, 0, 0, 0, 0, 0, -1, 1, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, 0, 1, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, 0, 1, -1, 0, 1, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0

Offset

1

Links

Table of n, a(n) for n=1..84.

Formula

The Möbius partition function muP(p) of a partition p is defined by: muP(p) = (-1)^k if p has k distinct parts; otherwise muP(p) = 0 (p is a partition in graded reverse lexicographic ordering).

Example

-1,
-1, 0,
-1, 1, 0,
-1, 1, 0, 0, 0,
-1, 1, 1, 0, 0,  0, 0,
-1, 1, 1, 0, 0, -1, 0, 0, 0, 0, 0,
-1, 1, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
...
Row 7 for partitions of 7 in the mentioned order: 7, 61, 52, 511, 43, 421, 4111, 331, 322, 3211, 31111, 2221, 22111, 211111, 1111111 with Möbius partition function.

Crossrefs

See A286349 for the Abramowitz-Stegun order.

Cf. A080577.

Sequence in context: A014555 A188017 A371931 * A286349 A145575 A077605

Adjacent sequences: A286752 A286753 A286754 * A286756 A286757 A286758

Keyword

sign

Author

Seiichi Manyama, May 13 2017

Status

approved