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

0,3

Links

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

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)

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 *)

Crossrefs

Row n=8 of A143324.

Cf. A090986, A013662, A267315.

Sequence in context: A324070 A145094 A239245 * A268637 A264317 A270174

Adjacent sequences: A218128 A218129 A218130 * A218132 A218133 A218134

Keyword

nonn,easy

Author

Alois P. Heinz, Oct 21 2012

Status

approved