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A218132
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Number of length 9 primitive (=aperiodic or period 9) n-ary words.
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2
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0, 0, 504, 19656, 262080, 1953000, 10077480, 40353264, 134217216, 387419760, 999999000, 2357946360, 5159778624, 10604497176, 20661044040, 38443356000, 68719472640, 118587871584, 198359284536, 322687690920, 511999992000, 794280037320, 1207269207144
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OFFSET
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0,3
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (10, -45, 120, -210, 252, -210, 120, -45, 10, -1).
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FORMULA
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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
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MAPLE
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a:= n-> (n^6-1)*n^3:
seq(a(n), n=0..30);
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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_Alois P. Heinz_, Oct 21 2012
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STATUS
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approved
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