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A329766
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Number of compositions of n whose run-lengths cover an initial interval of positive integers.
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19
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1, 1, 1, 3, 6, 13, 21, 48, 89, 180, 355, 707, 1382, 2758, 5448, 10786, 21391, 42476, 84291, 167516, 333036, 662153, 1317687, 2622706, 5221951, 10400350, 20720877, 41288823, 82294979, 164052035, 327088649, 652238016, 1300788712, 2594486045, 5175378128, 10324522020
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OFFSET
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0,4
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COMMENTS
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A composition of n is a finite sequence of positive integers with sum n.
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LINKS
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Table of n, a(n) for n=0..35.
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EXAMPLE
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The a(0) = 1 through a(5) = 13 compositions:
() (1) (2) (3) (4) (5)
(1,2) (1,3) (1,4)
(2,1) (3,1) (2,3)
(1,1,2) (3,2)
(1,2,1) (4,1)
(2,1,1) (1,1,3)
(1,2,2)
(1,3,1)
(2,1,2)
(2,2,1)
(3,1,1)
(1,1,2,1)
(1,2,1,1)
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MATHEMATICA
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normQ[m_]:=Or[m=={}, Union[m]==Range[Max[m]]];
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], normQ[Length/@Split[#]]&]], {n, 0, 10}]
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CROSSREFS
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Looking at multiplicities instead of run-lengths gives A329741.
The complete case is A329749.
Complete compositions are A107429.
Cf. A000740, A008965, A242882, A244164, A274174, A329738, A329739, A329740, A329744, A329748.
Sequence in context: A180750 A047172 A034734 * A019079 A280029 A178097
Adjacent sequences: A329763 A329764 A329765 * A329767 A329768 A329769
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KEYWORD
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nonn
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AUTHOR
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Gus Wiseman, Nov 20 2019
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EXTENSIONS
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a(21)-a(26) from Giovanni Resta, Nov 22 2019
a(27)-a(35) from Alois P. Heinz, Jul 06 2020
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STATUS
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approved
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