OFFSET
0,6
COMMENTS
A composition of n is a finite sequence of positive integers summing to n.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Unimodal Sequence.
EXAMPLE
The a(4) = 1 through a(6) = 14 compositions:
(121) (131) (132)
(212) (141)
(1121) (213)
(1211) (231)
(312)
(1131)
(1212)
(1221)
(1311)
(2112)
(2121)
(11121)
(11211)
(12111)
MATHEMATICA
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], !Or[LessEqual@@#, GreaterEqual@@#]&]], {n, 0, 10}]
PROG
(PARI) a(n)={if(n==0, 0, 2^(n-1) - 2*numbpart(n) + numdiv(n))} \\ Andrew Howroyd, Dec 30 2020
CROSSREFS
The version for unsorted prime signature is A332831.
The version for run-lengths of compositions is A332833.
The complement appears to be counted by A329398.
Unimodal compositions are A001523.
Compositions that are not unimodal are A115981.
Partitions with weakly increasing or decreasing run-lengths are A332745.
Compositions with weakly increasing or decreasing run-lengths are A332835.
Compositions with weakly increasing run-lengths are A332836.
Compositions that are neither unimodal nor is their negation are A332870.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 29 2020
STATUS
approved