|
|
A337481
|
|
Number of compositions of n that are neither strictly increasing nor strictly decreasing.
|
|
5
|
|
|
0, 0, 1, 1, 5, 11, 25, 55, 117, 241, 493, 1001, 2019, 4061, 8149, 16331, 32705, 65461, 130981, 262037, 524161, 1048425, 2096975, 4194097, 8388365, 16776933, 33554103, 67108481, 134217285, 268434945, 536870321, 1073741145, 2147482869, 4294966401, 8589933569
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,5
|
|
COMMENTS
|
A composition of n is a finite sequence of positive integers summing to n.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 2^(n-1) - 2*A000009(n) + 1, n > 0.
|
|
EXAMPLE
|
The a(2) = 1 through a(5) = 11 compositions:
(11) (111) (22) (113)
(112) (122)
(121) (131)
(211) (212)
(1111) (221)
(311)
(1112)
(1121)
(1211)
(2111)
(11111)
|
|
MATHEMATICA
|
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], !Less@@#&&!Greater@@#&]], {n, 0, 15}]
|
|
CROSSREFS
|
A337482 is the semi-strict version.
A337484 counts only compositions of length 3.
A218004 counts strictly increasing or weakly decreasing compositions.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|