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A337482 Number of compositions of n that are neither strictly increasing nor weakly decreasing. 7
0, 0, 0, 0, 2, 7, 18, 45, 101, 219, 461, 957, 1957, 3978, 8036, 16182, 32506, 65202, 130642, 261601, 523598, 1047709, 2096062, 4192946, 8386912, 16775117, 33551832, 67105663, 134213789, 268430636, 536865013, 1073734643, 2147474910, 4294956706, 8589921771 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
A composition of n is a finite sequence of positive integers summing to n.
LINKS
FORMULA
a(n) = 2^(n-1) - A000009(n) - A000041(n) + 1, n > 0.
EXAMPLE
The a(4) = 2 through a(4) = 18 compositions:
(112) (113) (114)
(121) (122) (132)
(131) (141)
(212) (213)
(1112) (231)
(1121) (312)
(1211) (1113)
(1122)
(1131)
(1212)
(1221)
(1311)
(2112)
(2121)
(11112)
(11121)
(11211)
(12111)
MATHEMATICA
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], !Less@@#&&!GreaterEqual@@#&]], {n, 0, 15}]
CROSSREFS
Ranked by the complement of the intersection of A114994 and A333255.
A128422 counts only the case of length 3.
A218004 counts the complement.
A332834 is the weak version.
A337481 is the strict version.
A001523 counts unimodal compositions, with complement counted by A115981.
A007318 and A097805 count compositions by length.
A032020 counts strict compositions, ranked by A233564.
A332745/A332835 count partitions/compositions with weakly increasing or weakly decreasing run-lengths.
Sequence in context: A037294 A076857 A243717 * A174192 A247289 A161870
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 11 2020
STATUS
approved

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Last modified March 3 03:04 EST 2024. Contains 370499 sequences. (Running on oeis4.)