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Expansion of 1/(1-x^8-x^9-x^10).
1

%I #16 Sep 08 2022 08:44:43

%S 1,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,1,2,3,2,1,0,0,0,1,3,6,7,6,3,1,0,1,4,

%T 10,16,19,16,10,4,2,5,15,30,45,51,45,30,16,11,22,50,90,126,141,126,91,

%U 57,49,83,162,266,357,393,358

%N Expansion of 1/(1-x^8-x^9-x^10).

%C Number of compositions (ordered partitions) of n into parts 8, 9 and 10. - _Ilya Gutkovskiy_, May 26 2017

%H Vincenzo Librandi, <a href="/A017868/b017868.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,1,1,1).

%F a(n) = a(n-8) +a(n-9) +a(n-10) for n>9. - _Vincenzo Librandi_, Jun 28 2013

%t CoefficientList[Series[1/(1 - Total[x^Range[8, 10]]), {x, 0, 70}], x] (* _Vincenzo Librandi_, Jun 28 2013 *)

%o (Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^8-x^9-x^10))); /* or */ I:=[1,0,0,0,0,0,0,0,1,1]; [n le 10 select I[n] else Self(n-8)+Self(n-9)+Self(n-10): n in [1..70]]; // _Vincenzo Librandi_, Jun 28 2013

%K nonn,easy

%O 0,18

%A _N. J. A. Sloane_.