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Number of length 9 primitive (=aperiodic or period 9) n-ary words.
2

%I #11 Jul 14 2015 10:40:37

%S 0,0,504,19656,262080,1953000,10077480,40353264,134217216,387419760,

%T 999999000,2357946360,5159778624,10604497176,20661044040,38443356000,

%U 68719472640,118587871584,198359284536,322687690920,511999992000,794280037320,1207269207144

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

%H Alois P. Heinz, <a href="/A218132/b218132.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10, -45, 120, -210, 252, -210, 120, -45, 10, -1).

%F 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.

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

%F 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

%p a:= n-> (n^6-1)*n^3:

%p seq(a(n), n=0..30);

%t 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 *)

%Y Row n=9 of A143324.

%K nonn,easy

%O 0,3

%A _Alois P. Heinz_, Oct 21 2012