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

0,3

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).

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

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 *)

Crossrefs

Row n=9 of A143324.

Sequence in context: A166763 A012829 A013973 * A012744 A291116 A145095

Adjacent sequences: A218129 A218130 A218131 * A218133 A218134 A218135

Keyword

nonn,easy

Author

Alois P. Heinz, Oct 21 2012

Status

approved