login
A335455
Number of compositions of n with some part appearing more than twice.
10
0, 0, 0, 1, 1, 5, 11, 30, 69, 142, 334, 740, 1526, 3273, 6840, 14251, 29029, 59729, 122009, 248070, 500649, 1012570, 2040238, 4107008, 8257466, 16562283, 33229788, 66621205, 133478437, 267326999, 535146239, 1071183438, 2143604313, 4289194948, 8581463248
OFFSET
0,6
COMMENTS
Also the number of compositions of n matching the pattern (1,1,1).
A composition of n is a finite sequence of positive integers summing to n.
FORMULA
a(n > 0) = 2^(n - 1) - A232432(n).
EXAMPLE
The a(3) = 1 through a(6) = 11 compositions:
(111) (1111) (1112) (222)
(1121) (1113)
(1211) (1131)
(2111) (1311)
(11111) (3111)
(11112)
(11121)
(11211)
(12111)
(21111)
(111111)
MATHEMATICA
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], Max@@Length/@Split[Sort[#]]>=3&]], {n, 0, 10}]
CROSSREFS
The case of partitions is A000726.
The avoiding version is A232432.
The (1,1)-matching version is A261982.
The version for patterns is A335508.
The version for prime indices is A335510.
These compositions are ranked by A335512.
Compositions are counted by A011782.
Combinatory separations are counted by A269134.
Normal patterns matched by compositions are counted by A335456.
Sequence in context: A179256 A209659 A266820 * A114688 A257717 A192194
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 15 2020
STATUS
approved