OFFSET
0,4
COMMENTS
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..500
Eric Weisstein's World of Mathematics, Unimodal Sequence.
EXAMPLE
The a(1) = 1 through a(9) = 8 partitions:
(1) (2) (3) (4) (5) (6) (7) (8) (9)
(21) (31) (32) (42) (43) (53) (54)
(41) (51) (52) (62) (63)
(321) (61) (71) (72)
(421) (521) (81)
(432)
(531)
(621)
For example, (4,3,1,0) has first differences (-1,-2,-1), which is not unimodal, so (4,3,1) is not counted under a(8).
MATHEMATICA
unimodQ[q_]:=Or[Length[q]<=1, If[q[[1]]<=q[[2]], unimodQ[Rest[q]], OrderedQ[Reverse[q]]]];
Table[Length[Select[IntegerPartitions[n], And[UnsameQ@@#, unimodQ[Differences[Append[#, 0]]]]&]], {n, 0, 30}]
CROSSREFS
The non-strict version is A332283.
The complement is counted by A332286.
Unimodal compositions are A001523.
Unimodal normal sequences appear to be A007052.
Unimodal permutations are A011782.
Partitions with unimodal run-lengths are A332280.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 21 2020
STATUS
approved