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Expansion of 1/(1-x^9-x^10-x^11-x^12).
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%I #22 Sep 25 2024 09:27:38

%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#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 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)

%o m:=70; R<x>:=PowerSeriesRing(Integers(), m);

%o Coefficients(R!(1/(1-x^9-x^10-x^11-x^12))); // _Vincenzo Librandi_, Jul 01 2013

%o (SageMath)

%o def A017879_list(prec):

%o P.<x> = PowerSeriesRing(ZZ, prec)

%o return P( (1-x)/(1-x-x^9+x^(13)) ).list()

%o A017879_list(85) # _G. C. Greubel_, Sep 25 2024

%Y Cf. A017877, A017878, A017880, A017881, A017882, A017883, A017884, A017885, A017886.

%K nonn,easy

%O 0,20

%A _N. J. A. Sloane_