OFFSET
1,7
COMMENTS
A Lyndon composition of n is a finite sequence summing to n that is lexicographically strictly less than all of its cyclic rotations. A co-Lyndon composition of n is a finite sequence summing to n that is lexicographically strictly greater than all of its cyclic rotations.
EXAMPLE
The a(6) = 1 through a(9) = 16 compositions:
(132) (142) (143) (153)
(1132) (152) (162)
(1142) (243)
(1232) (1143)
(1322) (1152)
(11132) (1242)
(11312) (1332)
(1422)
(11142)
(11232)
(11322)
(11412)
(12132)
(111132)
(111312)
(112212)
MATHEMATICA
lynQ[q_]:=Array[Union[{q, RotateRight[q, #1]}]=={q, RotateRight[q, #1]}&, Length[q]-1, 1, And];
colynQ[q_]:=Array[Union[{RotateRight[q, #1], q}]=={RotateRight[q, #1], q}&, Length[q]-1, 1, And];
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], lynQ[#]&&!colynQ[Reverse[#]]&]], {n, 15}]
CROSSREFS
Lyndon and co-Lyndon compositions are counted by A059966.
Numbers whose reversed binary expansion is Lyndon are A328596.
Numbers whose binary expansion is co-Lyndon are A275692.
Lyndon compositions that are not weakly increasing are A329141.
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Nov 11 2019
EXTENSIONS
a(21)-a(25) from Robert Price, Jun 20 2021
STATUS
approved