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A329766
Number of compositions of n whose run-lengths cover an initial interval of positive integers.
19
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
OFFSET
0,4
COMMENTS
A composition of n is a finite sequence of positive integers with sum n.
EXAMPLE
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)
MATHEMATICA
normQ[m_]:=Or[m=={}, Union[m]==Range[Max[m]]];
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], normQ[Length/@Split[#]]&]], {n, 0, 10}]
CROSSREFS
Looking at multiplicities instead of run-lengths gives A329741.
The complete case is A329749.
Complete compositions are A107429.
Sequence in context: A180750 A047172 A034734 * A019079 A280029 A178097
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 20 2019
EXTENSIONS
a(21)-a(26) from Giovanni Resta, Nov 22 2019
a(27)-a(35) from Alois P. Heinz, Jul 06 2020
STATUS
approved