OFFSET
0,7
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
EXAMPLE
The a(7) = 1 through a(12) = 11 compositions:
1111111 2222 333 22222 1112222 444
11111111 111222 1111222 2222111 3333
222111 2221111 11111222 111333
111111111 1111111111 22211111 222222
11111111111 333111
11112222
22221111
111111222
111222111
222111111
111111111111
MAPLE
b:= proc(n, h) option remember; `if`(n=0, 1, add(
`if`(i<>h, add(b(n-i*j, i), j=3..n/i), 0), i=1..n/3))
end:
a:= n-> b(n, 0):
seq(a(n), n=0..50); # Alois P. Heinz, May 17 2022
MATHEMATICA
Table[Length[Select[Join@@Permutations/@ IntegerPartitions[n], !MemberQ[Length/@Split[#], 1|2]&]], {n, 0, 15}]
CROSSREFS
The = 2 version is A003242 aerated.
The version for partitions is A100405.
A008466 counts compositions with some part > 2.
A011782 counts compositions.
A106356 counts compositions by number of adjacent equal parts.
A274174 counts compositions with equal parts contiguous.
A329739 counts compositions with all distinct run-lengths.
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 15 2022
EXTENSIONS
a(21)-a(49) from Alois P. Heinz, May 17 2022
STATUS
approved