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A011795 a(n) = floor(C(n,4)/5). 7
0, 0, 0, 0, 0, 1, 3, 7, 14, 25, 42, 66, 99, 143, 200, 273, 364, 476, 612, 775, 969, 1197, 1463, 1771, 2125, 2530, 2990, 3510, 4095, 4750, 5481, 6293, 7192, 8184, 9275, 10472, 11781, 13209, 14763, 16450, 18278 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

a(n-1)=number of aperiodic necklaces (Lyndon words) with 5 black beads and n-5 white beads.

REFERENCES

J. M. Borwein, D. H. Bailey and R. Girgensohn, Experimentation in Mathematics, A K Peters, Ltd., Natick, MA, 2004. x+357 pp. See p. 147.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

D. 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.

Index entries for sequences related to Lyndon words

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1,1,-4,6,-4,1).

FORMULA

G.f.: x^5(1+x^3)/((1-x)^3(1-x^2)(1-x^5)) = x^5*(1-x+x^2)/((1-x)^5*(1+x+x^2+x^3+x^4)).

a(n) = floor(binomial(n+1,5)/(n+1)). - Gary Detlefs Nov 23 2011

MAPLE

seq(floor(binomial(n, 4)/5), n=0.. 40); # Zerinvary Lajos, Jan 12 2009

MATHEMATICA

CoefficientList[Series[x^5(1+x^3)/((1-x)^3(1-x^2)(1-x^5))=x^5*(1-x+x^2)/((1-x)^5*(1+x+x^2+x^3+x^4)), {x, 0, 50}], x] (* Vincenzo Librandi, Jun 19 2012 *)

CoefficientList[Series[x^4/5 (1/(1-x)^5-1/(1- x^5)), {x, 0, 50}], x] (* Herbert Kociemba, Oct 16 2016 *)

PROG

(MAGMA) [Floor(Binomial(n+1, 5)/(n+1)): n in [0..45]]; // Vincenzo Librandi Jun 19 2012

(PARI) a(n)=binomial(n, 4)\5 \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

Cf. A000031, A001037, A051168. Same as A051170(n+1).

A column of triangle A011847.

Sequence in context: A089240 A057524 A293467 * A051170 A265252 A193911

Adjacent sequences:  A011792 A011793 A011794 * A011796 A011797 A011798

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, David Broadhurst

STATUS

approved

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Last modified October 20 06:43 EDT 2018. Contains 316378 sequences. (Running on oeis4.)