login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Table of n, a(n) for n=1..20.

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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