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A017879 Expansion of 1/(1-x^9-x^10-x^11-x^12).

%I A017879 #22 Sep 25 2024 09:27:38
%S A017879 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 A017879 10,6,3,2,4,10,20,31,40,44,40,31,21,15,19,36,65,101,135,155,155,136,
%U A017879 107,86,91,135,221,337,456,546
%N A017879 Expansion of 1/(1-x^9-x^10-x^11-x^12).
%C A017879 Number of compositions (ordered partitions) of n into parts 9, 10, 11 and 12. - _Ilya Gutkovskiy_, May 27 2017
%H A017879 Vincenzo Librandi, <a href="/A017879/b017879.txt">Table of n, a(n) for n = 0..1000</a>
%H A017879 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,1,1,1,1).
%F A017879 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 A017879 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 A017879 CoefficientList[Series[1/(1 - Total[x^Range[9, 12]]), {x,0,70}], x] (* _Vincenzo Librandi_, Jul 01 2013 *)
%o A017879 (Magma)
%o A017879 m:=70; R<x>:=PowerSeriesRing(Integers(), m);
%o A017879 Coefficients(R!(1/(1-x^9-x^10-x^11-x^12))); // _Vincenzo Librandi_, Jul 01 2013
%o A017879 (SageMath)
%o A017879 def A017879_list(prec):
%o A017879     P.<x> = PowerSeriesRing(ZZ, prec)
%o A017879     return P( (1-x)/(1-x-x^9+x^(13)) ).list()
%o A017879 A017879_list(85) # _G. C. Greubel_, Sep 25 2024
%Y A017879 Cf. A017877, A017878, A017880, A017881, A017882, A017883, A017884, A017885, A017886.
%K A017879 nonn,easy
%O A017879 0,20
%A A017879 _N. J. A. Sloane_