A011797 a(n) = floor(C(n,6)/7).

0, 0, 0, 0, 0, 0, 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

Offset

0,9

Comments

a(n-1) is the number of aperiodic necklaces (Lyndon words) with 7 black beads and n-7 white beads.

Links

Table of n, a(n) for n=0..36.

David J. Broadhurst, On the enumeration of irreducible k-fold Euler sums and their roles in knot theory and field theory, arXiv:hep-th/9604128, 1996.

David Broadhurst and Xavier Roulleau, Number of partitions of modular integers, arXiv:2502.19523 [math.NT], 2025. See p. 19.

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.: (1+x^3)^2/((1-x)^4(1-x^2)^2(1-x^7))*x^7.

a(n) = floor(binomial(n+1,7)/(n+1)). [Gary Detlefs, Nov 23 2011]

G.f.: (x^6/7)*(1/(1-x)^7-1/(1- x^7)). - Herbert Kociemba, Oct 16 2016

Mathematica

CoefficientList[Series[x^6/7 (1/(1-x)^7-1/(1- x^7)), {x, 0, 40}], x]; (* Herbert Kociemba, Oct 16 2016 *)

Prog

(PARI) a(n) = binomial(n, 6)\7; \\ Michel Marcus, Oct 16 2016

Crossrefs

Cf. A000031, A001037, A051168. Same as A051172(n+1).

First differences of A011853.

A column of triangle A011847.

Sequence in context: A166213 A274250 A004036 * A051172 A032192 A212587

Adjacent sequences: A011794 A011795 A011796 * A011798 A011799 A011800

Keyword

nonn,easy

Author

N. J. A. Sloane, David Broadhurst

Status

approved