OFFSET
0,7
COMMENTS
Also the number of compositions of n into distinct terms whose negation is not unimodal. - Gus Wiseman, Mar 05 2020
LINKS
Eric Weisstein's World of Mathematics, Unimodal Sequence
EXAMPLE
a(6)=2 since 6 can be written as 2+1+3 or 3+1+2.
From Gus Wiseman, Mar 05 2020: (Start)
The a(6) = 2 through a(9) = 6 strict compositions:
(2,1,3) (2,1,4) (2,1,5) (2,1,6)
(3,1,2) (4,1,2) (3,1,4) (3,1,5)
(4,1,3) (3,2,4)
(5,1,2) (4,2,3)
(5,1,3)
(6,1,2)
(End)
MATHEMATICA
unimodQ[q_]:=Or[Length[q]<=1, If[q[[1]]<=q[[2]], unimodQ[Rest[q]], OrderedQ[Reverse[q]]]];
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], UnsameQ@@#&&!unimodQ[#]&]], {n, 0, 16}] (* Gus Wiseman, Mar 05 2020 *)
CROSSREFS
The complement is counted by A072706.
The non-strict version is A115981.
The case where the negation is not unimodal either is A332874.
Unimodal compositions are A001523.
Strict compositions are A032020.
Non-unimodal permutations are A059204.
A triangle for strict unimodal compositions is A072705.
Non-unimodal sequences covering an initial interval are A328509.
Numbers whose prime signature is not unimodal are A332282.
Strict partitions whose 0-appended differences are not unimodal are A332286.
Compositions whose negation is unimodal are A332578.
Compositions whose negation is not unimodal are A332669.
Non-unimodal compositions covering an initial interval are A332743.
KEYWORD
nonn,changed
AUTHOR
Henry Bottomley, Jul 04 2002
STATUS
approved