

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
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OFFSET

0,5


COMMENTS

A composition of n is a finite sequence of positive integers summing to n.


LINKS



FORMULA



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

A128422 counts only the case of length 3.
A001523 counts unimodal compositions, with complement counted by A115981.
A332745/A332835 count partitions/compositions with weakly increasing or weakly decreasing runlengths.


KEYWORD

nonn


AUTHOR



STATUS

approved



