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A353400
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Number of integer compositions of n with all run-lengths > 2.
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10
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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
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OFFSET
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0,7
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LINKS
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EXAMPLE
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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
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MAPLE
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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):
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MATHEMATICA
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Table[Length[Select[Join@@Permutations/@ IntegerPartitions[n], !MemberQ[Length/@Split[#], 1|2]&]], {n, 0, 15}]
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CROSSREFS
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The = 2 version is A003242 aerated.
The version for parts instead of run-lengths is A078012, both A353428.
The version for partitions is A100405.
A008466 counts compositions with some part > 2.
A106356 counts compositions by number of adjacent equal parts.
A274174 counts compositions with equal parts contiguous.
A329739 counts compositions with all distinct run-lengths.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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