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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

A composition of n is a finite sequence of positive integers with sum n.

LINKS

Table of n, a(n) for n=0..35.

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.

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

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

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Last modified April 16 18:53 EDT 2021. Contains 343050 sequences. (Running on oeis4.)