A051172 T(n,7), array T as in A051168; a count of Lyndon words; aperiodic necklaces with 7 black beads and n-7 white beads.

0, 1, 4, 12, 30, 66, 132, 245, 429, 715, 1144, 1768, 2652, 3876, 5537, 7752, 10659, 14421, 19228, 25300, 32890, 42287, 53820, 67860, 84825, 105183, 129456, 158224, 192129, 231880, 278256, 332112, 394383, 466089, 548340

Offset: 7

Author

Clark Kimberling

Keywords

• nonn

Links

• Index entries for sequences related to Lyndon words
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1,1,-6,15,-20,15,-6,1).

Crossrefs

Cf. A000031, A001037, A051168. Same as A011797(n-1).

Programs

Mathematica

Drop[CoefficientList[Series[-(x^7/7)*(1/(1-x^7)+1/(-1+x)^7),{x,0,50}],x],7] (* Harvey P. Dale, Aug 04 2024 *)

Formula

G.f.: -(x^7/7)*(1/(1- x^7)+1/(-1+x)^7). - Herbert Kociemba, Oct 16 2016

Extensions

a(20) corrected by Herbert Kociemba, Oct 16 2016