cp's OEIS Frontend

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

%I A218131 #14 Jan 12 2021 05:59:37
%S A218131 0,0,240,6480,65280,390000,1678320,5762400,16773120,43040160,99990000,
%T A218131 214344240,429960960,815702160,1475750640,2562840000,4294901760,
%U A218131 6975673920,11019855600,16983432720,25599840000,37822664880,54875639280,78310705440,110074982400
%N A218131 Number of length 8 primitive (=aperiodic or period 8) n-ary words.
%H A218131 Alois P. Heinz, <a href="/A218131/b218131.txt">Table of n, a(n) for n = 0..1000</a>
%F A218131 G.f.: -240*x^2*(x+1)*(x^4+17*x^3+48*x^2+17*x+1)/(x-1)^9.
%F A218131 a(n) = n^8-n^4.
%F A218131 From _Amiram Eldar_, Jan 12 2021: (Start)
%F A218131 Sum_{n>=2} 1/a(n) = 15/8 - Pi^4/90 - Pi*coth(Pi)/4.
%F A218131 Sum_{n>=2} (-1)^n/a(n) = -7/8 + 7*Pi^4/720 - Pi*csch(Pi)/4 = -7/8 + A267315 - (1/4) * A090986. (End)
%p A218131 a:= n-> (n^4-1)*n^4:
%p A218131 seq(a(n), n=0..30);
%t A218131 Table[n^8 - n^4, {n, 0, 30}] (* _Wesley Ivan Hurt_, Mar 30 2017 *)
%Y A218131 Row n=8 of A143324.
%Y A218131 Cf. A090986, A013662, A267315.
%K A218131 nonn,easy
%O A218131 0,3
%A A218131 _Alois P. Heinz_, Oct 21 2012