OFFSET
0,4
FORMULA
a(n) = 2^(n-1) - A000009(n) for n > 0.
EXAMPLE
The a(2) = 1 through a(5) = 13 compositions:
(11) (21) (22) (32)
(111) (31) (41)
(112) (113)
(121) (122)
(211) (131)
(1111) (212)
(221)
(311)
(1112)
(1121)
(1211)
(2111)
(11111)
MATHEMATICA
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], !Less@@#&]], {n, 0, 15}]
CROSSREFS
A000009 counts the complement.
A047967 is the unordered version.
A056823 is the weak version.
A140106 counts the unordered case of length 3.
A242771 counts the case of length 3.
A333255 is the complement of a ranking sequence (using standard compositions A066099) for these compositions.
A337481 counts these compositions that are not strictly decreasing.
A337482 counts these compositions that are not weakly decreasing.
A218004 counts strictly increasing or weakly decreasing compositions.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 06 2020
STATUS
approved