OFFSET
0,8
COMMENTS
A sequence of positive integers is unimodal if it is the concatenation of a weakly increasing and a weakly decreasing sequence.
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..400
Eric Weisstein's World of Mathematics, Unimodal Sequence.
EXAMPLE
The a(6) = 1 through a(11) = 18 partitions:
(2211) (331) (431) (441) (541) (551)
(22111) (3311) (4311) (3322) (641)
(22211) (32211) (3331) (4331)
(221111) (33111) (4411) (4421)
(222111) (33211) (5411)
(2211111) (42211) (33221)
(43111) (33311)
(222211) (44111)
(322111) (52211)
(331111) (322211)
(2221111) (332111)
(22111111) (422111)
(431111)
(2222111)
(3221111)
(3311111)
(22211111)
(221111111)
MATHEMATICA
unimodQ[q_]:=Or[Length[q]<=1, If[q[[1]]<=q[[2]], unimodQ[Rest[q]], OrderedQ[Reverse[q]]]];
Table[Length[Select[IntegerPartitions[n], !unimodQ[Differences[Append[#, 0]]]&]], {n, 30}]
CROSSREFS
The complement is counted by A332283.
The strict version is A332286.
The Heinz numbers of these partitions are A332287.
Non-unimodal permutations are A059204.
Non-unimodal compositions are A115981.
Non-unimodal normal sequences appear to be A328509.
Partitions with non-unimodal run-lengths are A332281.
Heinz numbers of partitions with non-unimodal run-lengths are A332282.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 20 2020
STATUS
approved