A218131 Number of length 8 primitive (=aperiodic or period 8) n-ary words.

0, 0, 240, 6480, 65280, 390000, 1678320, 5762400, 16773120, 43040160, 99990000, 214344240, 429960960, 815702160, 1475750640, 2562840000, 4294901760, 6975673920, 11019855600, 16983432720, 25599840000, 37822664880, 54875639280, 78310705440, 110074982400

Offset: 0

Author

Alois P. Heinz, Oct 21 2012

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Row n=8 of A143324.

Cf. A090986, A013662, A267315.

Programs

Maple

a:= n-> (n^4-1)*n^4:
seq(a(n), n=0..30);

Mathematica

Table[n^8 - n^4, {n, 0, 30}] (* Wesley Ivan Hurt, Mar 30 2017 *)

Formula

G.f.: -240*x^2*(x+1)*(x^4+17*x^3+48*x^2+17*x+1)/(x-1)^9.

a(n) = n^8-n^4.

From Amiram Eldar, Jan 12 2021: (Start)

Sum_{n>=2} 1/a(n) = 15/8 - Pi^4/90 - Pi*coth(Pi)/4.

Sum_{n>=2} (-1)^n/a(n) = -7/8 + 7*Pi^4/720 - Pi*csch(Pi)/4 = -7/8 + A267315 - (1/4) * A090986. (End)