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%I #18 Sep 08 2022 08:44:43
%S 1,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,1,2,3,4,3,2,1,0,0,1,3,6,10,12,12,
%T 10,6,3,2,4,10,20,31,40,44,40,31,21,15,19,36,65,101,135,155,155,136,
%U 107,86,91,135,221,337,456,546
%N Expansion of 1/(1-x^9-x^10-x^11-x^12).
%C Number of compositions (ordered partitions) of n into parts 9, 10, 11 and 12. - _Ilya Gutkovskiy_, May 27 2017
%H Vincenzo Librandi, <a href="/A017879/b017879.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 (0,0,0,0,0,0,0,0,1,1,1,1).
%F a(0)=1, a(1)=0, a(2)=0, a(3)=0, a(4)=0, a(5)=0, a(6)=0, a(7)=0, a(8)=0, a(9)=1, a(10)=1, a(11)=1; for n>11, a(n) = a(n-9)+a(n-10)+a(n-11)+a(n-12). - _Harvey P. Dale_, Apr 29 2013
%t CoefficientList[Series[1 / (1 - x^9 - x^10 - x^11 - x^12), {x, 0, 70}], x] (* or *) LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1}, {1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1}, 70] (* _Harvey P. Dale_, Apr 29 2013 *)
%t CoefficientList[Series[1 / (1 - Total[x^Range[9, 12]]), {x, 0, 70}], x] (* _Vincenzo Librandi_, Jul 01 2013 *)
%o (Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^9-x^10-x^11-x^12))); /* or */ I:=[1,0,0,0,0,0,0,0,0,1,1,1]; [n le 12 select I[n] else Self(n-9)+Self(n-10)+Self(n-11)+Self(n-12): n in [1..70]]; // _Vincenzo Librandi_, Jul 01 2013
%K nonn,easy
%O 0,20
%A _N. J. A. Sloane_.
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