%I #21 Sep 08 2022 08:44:43
%S 1,0,0,1,1,1,2,3,4,6,9,12,18,27,38,55,81,117,169,246,357,517,751,1090,
%T 1580,2293,3328,4827,7003,10162,14743,21389,31034,45026,65325,94779,
%U 137512,199509,289461,419970,609317
%N Expansion of 1/(1-x^3-x^4-x^5-x^6-x^7-x^8-x^9-x^10).
%C Number of compositions of n into parts p where 3 <= p <= 10. - _Joerg Arndt_, Jun 27 2013
%H Vincenzo Librandi, <a href="/A017823/b017823.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 (0,0,1,1,1,1,1,1,1,1).
%F a(0)=1, a(1)=0, a(2)=0, a(3)=1, a(4)=1, a(5)=1, a(6)=2, a(7)=3, a(8)=4, a(9)=6, a(n)=a(n-3)+a(n-4)+a(n-5)+a(n-6)+a(n-7)+a(n-8)+a(n-9)+a(n-10). - _Harvey P. Dale_, Feb 14 2012
%t CoefficientList[Series[1/(1+Total[-x^Range[3,10]]),{x,0,40}],x] (* or *) LinearRecurrence[{0,0,1,1,1,1,1,1,1,1},{1,0,0,1,1,1,2,3,4,6},41] (* _Harvey P. Dale_, Feb 14 2012 *)
%o (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^3-x^4-x^5-x^6-x^7-x^8-x^9-x^10))); /* or */ I:=[1, 0, 0, 1, 1, 1, 2, 3, 4, 6]; [n le 10 select I[n] else Self(n-3)+Self(n-4)+Self(n-5)+Self(n-6)+Self(n-7)+Self(n-8)+Self(n-9)+Self(n-10): n in [1..50]]; // _Vincenzo Librandi_, Jun 27 2013
%K nonn,easy
%O 0,7
%A _N. J. A. Sloane_.