A329141 - OEIS

A329141

Number of Lyndon compositions of n that are not weakly increasing.

0, 0, 0, 0, 0, 1, 4, 11, 28, 60, 131, 263, 530, 1029, 2009, 3853, 7414, 14152, 27105, 51755, 99069, 189558, 363468, 697302, 1340220, 2578362, 4968001, 9582682, 18508226, 35784670, 69266825, 134207336, 260290846, 505274108, 981691926

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OFFSET

1,7

COMMENTS

A Lyndon composition of n is a finite sequence of positive integers summing to n that is lexicographically strictly less than all of its cyclic rotations.

LINKS

Table of n, a(n) for n=1..35.

FORMULA

a(n) = A059966(n) - A167934(n).

EXAMPLE

The a(6) = 1 through a(8) = 11 compositions:

(132) (142) (143)

(1132) (152)

(1213) (1142)

(11212) (1214)

(1232)

(1322)

(11132)

(11213)

(11312)

(12122)

(111212)

MATHEMATICA

neckQ[q_]:=Array[OrderedQ[{q, RotateRight[q, #]}]&, Length[q]-1, 1, And];

aperQ[q_]:=Array[RotateRight[q, #1]&, Length[q], 1, UnsameQ];

Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], !OrderedQ[#]&&neckQ[#]&&aperQ[#]&]], {n, 10}]

CROSSREFS

Lyndon compositions are A059966.

Lyndon compositions that are weakly increasing are A167934.

Binary Lyndon words are A001037.

Necklace compositions are A008965.

Cf. A000031, A000740, A178472, A318731, A328596, A329131, A329145.

Sequence in context: A031127 A239031 A289217 * A090539 A262050 A293628

Adjacent sequences: A329138 A329139 A329140 * A329142 A329143 A329144

KEYWORD

nonn

AUTHOR

Gus Wiseman, Nov 10 2019

STATUS

approved