A051170 T(n,5), array T as in A051168; a count of Lyndon words; aperiodic necklaces with 5 black beads and n-5 white beads.

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, 20254, 22386, 24682

Offset

5,3

Links

G. C. Greubel, Table of n, a(n) for n = 5..5000

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^6*(x^2-x+1) / ((x-1)^5*(x^4+x^3+x^2+x+1)). - Colin Barker, Jun 05 2013

a(n) = floor(C(n,5)/n). - Alois P. Heinz, Jun 05 2013

G.f.: x^5/5 * (1/(1-x)^5 - 1/(1-x^5)). - Herbert Kociemba, Oct 16 2016

Mathematica

Table[Floor[Binomial[n, 5]/n], {n, 5, 50}] (* G. C. Greubel, Nov 26 2017 *)

Prog

(PARI) for(n=5, 30, print1(floor(binomial(n, 5)/n), ", ")) \\ G. C. Greubel, Nov 26 2017
(Magma) [ Floor(Binomial(n, 5)/n): n in [5..30]]; // G. C. Greubel, Nov 26 2017

Crossrefs

Cf. A000031, A001037, A051168. Same as A011795(n-1).

First differences of A036837.

Sequence in context: A057524 A293467 A011795 * A265252 A193911 A206417

Adjacent sequences: A051167 A051168 A051169 * A051171 A051172 A051173

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved