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

7,3

Links

Table of n, a(n) for n=7..41.

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).

Formula

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

a(n) = n^6/5040 - n^5/240 + 5/144*n^4 - 7/48*n^3 + 29/90*n^2 - 7/20*n + O(1). - Charles R Greathouse IV, Jun 02 2026

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 *)

Prog

(PARI) a(n)=(n^6-21*n^5+175*n^4-735*n^3+1624*n^2-1764*n+bittest(126, n%7)*720)/5040 \\ Charles R Greathouse IV, Jun 02 2026

Crossrefs

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

Sequence in context: A274250 A004036 A011797 * A032192 A212587 A338223

Adjacent sequences: A051169 A051170 A051171 * A051173 A051174 A051175

Keyword

nonn,easy

Author

Clark Kimberling

Extensions

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

Status

approved