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A329324
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Number of Lyndon compositions of n whose reverse is not a co-Lyndon composition.
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13
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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
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OFFSET
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1,7
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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)
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MATHEMATICA
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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}]
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CROSSREFS
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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.
Cf. A000740, A001037, A008965, A060223, A102659, A211100, A329131, A329312, A329313, A329318, A329326.
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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