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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 (list; graph; refs; listen; history; text; internal format)
 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. LINKS 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. Cf. A000740, A001037, A008965, A060223, A102659, A211100, A329131, A329312, A329313, A329318, A329326. Sequence in context: A259966 A283500 A097442 * A131405 A269963 A176805 Adjacent sequences:  A329321 A329322 A329323 * A329325 A329326 A329327 KEYWORD nonn,more AUTHOR Gus Wiseman, Nov 11 2019 STATUS approved

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Last modified May 12 03:56 EDT 2021. Contains 343810 sequences. (Running on oeis4.)