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

Author

Clark Kimberling

Keywords

• nonn
• easy

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).

Crossrefs

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

First differences of A036837.

Programs

Magma

[ Floor(Binomial(n,5)/n): n in [5..30]]; // G. C. Greubel, Nov 26 2017

Mathematica

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

PARI

for(n=5,30, print1(floor(binomial(n,5)/n), ", ")) \\ G. C. Greubel, Nov 26 2017

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