OFFSET
0,7
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
EXAMPLE
The a(0) = 1 through a(14) = 11 compositions (empty columns indicated by dots, 0 is the empty composition):
0 . . . 22 . 33 . 44 333 55 . 66 22333 77
222 2222 2233 444 33322 2255
3322 2244 3344
22222 3333 4433
4422 5522
22233 22244
33222 44222
222222 222233
223322
332222
2222222
MAPLE
b:= proc(n, h) option remember; `if`(n=0, 1, add(
`if`(i<>h, add(b(n-i*j, i), j=2..n/i), 0), i=2..n/2))
end:
a:= n-> b(n, 0):
seq(a(n), n=0..60); # Alois P. Heinz, May 17 2022
MATHEMATICA
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], !MemberQ[#, 1]&&!MemberQ[Length/@Split[#], 1]&]], {n, 0, 15}]
CROSSREFS
The version for partitions is A339222.
Compositions counted by their run-lengths:
- For run-lengths = 2 we have A003242 aerated.
- For run-lengths all prime we have A353401.
- For run-lengths and parts > 2 we have A353428.
A008466 counts compositions with some part > 2.
A011782 counts compositions.
A106356 counts compositions by number of adjacent equal parts.
A261983 counts non-anti-run compositions.
A274174 counts compositions with equal parts contiguous.
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 17 2022
EXTENSIONS
a(41)-a(52) from Alois P. Heinz, May 17 2022
STATUS
approved