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A017880 Expansion of 1/(1-x^9-x^10-x^11-x^12-x^13).

%I A017880 #24 Sep 25 2024 09:30:55
%S A017880 1,0,0,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,1,2,3,4,5,4,3,2,1,1,3,6,10,15,18,
%T A017880 19,18,15,11,10,13,21,35,52,68,80,85,81,73,67,70,90,131,189,256,320,
%U A017880 366,387,386,376,381,431,547
%N A017880 Expansion of 1/(1-x^9-x^10-x^11-x^12-x^13).
%C A017880 Number of compositions (ordered partitions) of n into parts 9, 10, 11, 12 and 13. - _Ilya Gutkovskiy_, May 27 2017
%H A017880 Vincenzo Librandi, <a href="/A017880/b017880.txt">Table of n, a(n) for n = 0..1000</a>
%H A017880 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,1,1,1,1,1).
%F A017880 a(n) = a(n-9) +a(n-10) +a(n-11) +a(n-12) +a(n-13) for n>12. - _Vincenzo Librandi_, Jul 01 2013
%t A017880 CoefficientList[Series[1 / (1 - Total[x^Range[9, 13]]), {x, 0, 80}], x] (* _Vincenzo Librandi_, Jul 01 2013 *)
%t A017880 LinearRecurrence[{0,0,0,0,0,0,0,0,1,1,1,1,1},{1,0,0,0,0,0,0,0,0,1,1,1,1},70] (* _Harvey P. Dale_, Apr 03 2018 *)
%o A017880 (Magma)
%o A017880 m:=70; R<x>:=PowerSeriesRing(Integers(), m);
%o A017880 Coefficients(R!(1/(1-x^9-x^10-x^11-x^12-x^13))); // _Vincenzo Librandi_, Jul 01 2013
%o A017880 (SageMath)
%o A017880 def A017880_list(prec):
%o A017880     P.<x> = PowerSeriesRing(ZZ, prec)
%o A017880     return P( (1-x)/(1-x-x^9+x^(14)) ).list()
%o A017880 A017880_list(80) # _G. C. Greubel_, Sep 25 2024
%Y A017880 Cf. A017877, A017878, A017879, A017881, A017882, A017883, A017884, A017885, A017886.
%K A017880 nonn,easy
%O A017880 0,20
%A A017880 _N. J. A. Sloane_