|
|
A332870
|
|
Number of compositions of n that are neither unimodal nor is their negation.
|
|
16
|
|
|
0, 0, 0, 0, 0, 0, 2, 9, 32, 92, 243, 587, 1361, 3027, 6564, 13928, 29127, 60180, 123300, 250945, 508326, 1025977, 2065437, 4150056, 8327344, 16692844, 33438984, 66951671, 134004892, 268148573, 536486146, 1073227893, 2146800237, 4294061970, 8588740071, 17178298617
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,7
|
|
COMMENTS
|
A sequence of integers is unimodal if it is the concatenation of a weakly increasing and a weakly decreasing sequence.
A composition of n is a finite sequence of positive integers summing to n.
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
The a(6) = 2 and a(7) = 9 compositions:
(1212) (1213)
(2121) (1312)
(2131)
(3121)
(11212)
(12112)
(12121)
(21121)
(21211)
|
|
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], !unimodQ[#]&&!unimodQ[-#]&]], {n, 0, 10}]
|
|
CROSSREFS
|
The case of run-lengths of partitions is A332640.
The version for unsorted prime signature is A332643.
Non-unimodal compositions are A115981.
Non-unimodal normal sequences are A328509.
Compositions whose negation is unimodal are A332578.
Compositions whose negation is not unimodal are A332669.
Partitions with weakly increasing or decreasing run-lengths are A332745.
Compositions that are neither weakly increasing nor decreasing are A332834.
Compositions with weakly increasing or decreasing run-lengths are A332835.
Cf. A000005, A000041, A007052, A072704, A227038, A329398, A332281, A332284, A332639, A332641, A332746, A332831, A332833.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|