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%I #17 Sep 08 2022 08:44:43
%S 1,0,0,0,0,0,0,1,1,1,0,0,0,0,1,2,3,2,1,0,0,1,3,6,7,6,3,1,1,4,10,16,19,
%T 16,10,5,6,15,30,45,51,45,31,21,26,51,90,126,141,127,97,78,98,167,267,
%U 357,394,365,302,273,343,532
%N Expansion of 1/(1-x^7-x^8-x^9).
%C Number of compositions of n into parts 7, 8, and 9. [_Joerg Arndt_, Jun 28 2013]
%H Vincenzo Librandi, <a href="/A017858/b017858.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 (0,0,0,0,0,0,1,1,1).
%F a(0)=1, a(1)=0, a(2)=0, a(3)=0, a(4)=0, a(5)=0, a(6)=0, a(7)=1, a(8)=1; for n>8, a(n) = a(n-7)+a(n-8)+a(n-9). - _Harvey P. Dale_, Aug 17 2012
%t CoefficientList[Series[1 / (1 - x^7 - x^8 - x^9),{x, 0, 70}], x] (* or *) LinearRecurrence[{0, 0, 0, 0, 0, 0, 1, 1, 1}, {1, 0, 0, 0, 0, 0, 0, 1, 1}, 70] (* _Harvey P. Dale_, Aug 17 2012 *)
%t CoefficientList[Series[1 / (1 - Total[x^Range[7, 9]]), {x, 0, 70}], x] (* _Vincenzo Librandi_, Jun 28 2013 *)
%o (Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^7-x^8-x^9))); /* or */ I:=[1,0,0,0,0,0,0,1,1]; [n le 9 select I[n] else Self(n-7)+Self(n-8)+Self(n-9): n in [1..70]]; // _Vincenzo Librandi_, Jun 28 2013
%K nonn,easy
%O 0,16
%A _N. J. A. Sloane_.
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