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A286755
Möbius (or Moebius) partition function of partitions in graded reverse lexicographic ordering.
0
-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
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
KEYWORD
sign
AUTHOR
Seiichi Manyama, May 13 2017
STATUS
approved