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A329324
Number of Lyndon compositions of n whose reverse is not a co-Lyndon composition.
13
0, 0, 0, 0, 0, 1, 2, 7, 16, 37, 76, 166, 328, 669, 1326, 2626, 5138, 10104, 19680, 38442, 74822, 145715, 283424, 551721, 1073224
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.
Sequence in context: A283500 A097442 A345025 * A131405 A269963 A176805
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Nov 11 2019
EXTENSIONS
a(21)-a(25) from Robert Price, Jun 20 2021
STATUS
approved