A218132 Number of length 9 primitive (=aperiodic or period 9) n-ary words.

0, 0, 504, 19656, 262080, 1953000, 10077480, 40353264, 134217216, 387419760, 999999000, 2357946360, 5159778624, 10604497176, 20661044040, 38443356000, 68719472640, 118587871584, 198359284536, 322687690920, 511999992000, 794280037320, 1207269207144

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
• Index entries for linear recurrences with constant coefficients, signature (10, -45, 120, -210, 252, -210, 120, -45, 10, -1).

Crossrefs

Row n=9 of A143324.

Programs

Maple

a:= n-> (n^6-1)*n^3:
seq(a(n), n=0..30);

Mathematica

Table[n^9-n^3,{n,0,40}] (* or *) LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{0,0,504,19656,262080,1953000,10077480,40353264,134217216,387419760},40] (* Harvey P. Dale, Feb 11 2015 *)

Formula

G.f.: 504*x^2*(x^6+29*x^5+175*x^4+310*x^3+175*x^2+29*x+1)/(x-1)^10.

a(n) = n^9-n^3.

a(0)=0, a(1)=0, a(2)=504, a(3)=19656, a(4)=262080, a(5)=1953000, a(6)=10077480, a(7)=40353264, a(8)=134217216, a(9)=387419760, a(n)=10*a(n-1)- 45*a(n-2)+120*a(n-3)-210*a(n-4)+252*a(n-5)- 210*a(n-6)+ 120*a(n-7)-45*a(n-8)+10*a(n-9)-a(n-10). - Harvey P. Dale, Feb 11 2015