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A353400
Number of integer compositions of n with all run-lengths > 2.
10
1, 0, 0, 1, 1, 1, 2, 1, 2, 4, 4, 5, 11, 11, 14, 27, 29, 37, 61, 72, 97, 147, 181, 246, 368, 470, 632, 914, 1198, 1611, 2286, 3018, 4079, 5709, 7619, 10329, 14333, 19258, 26142, 36069, 48688, 66114, 90800, 122913, 167020, 228735, 310167, 421708, 576499, 782803
OFFSET
0,7
LINKS
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 <= 1 version is A003242 ranked by A333489.
The version for parts instead of run-lengths is A078012, both A353428.
The version for partitions is A100405.
The > 1 version is A114901, ranked by A353427.
The <= 2 version is A128695, matching A335464.
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.
A329738 counts uniform compositions, partitions A047966.
A329739 counts compositions with all distinct run-lengths.
Sequence in context: A073252 A134005 A132320 * A076369 A328790 A319773
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 15 2022
EXTENSIONS
a(21)-a(49) from Alois P. Heinz, May 17 2022
STATUS
approved