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A329141
Number of Lyndon compositions of n that are not weakly increasing.
6
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
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.
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.
Sequence in context: A031127 A239031 A289217 * A090539 A262050 A293628
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 10 2019
STATUS
approved