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A017885 Expansion of 1/(1-x^9-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17-x^18).

%I A017885 #20 Sep 25 2024 15:50:10
%S A017885 1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,2,2,3,4,5,6,7,8,9,11,12,14,17,21,
%T A017885 26,32,39,47,57,67,79,93,110,131,157,189,228,276,332,399,478,571,681,
%U A017885 812,969,1158,1387,1662,1994
%N A017885 Expansion of 1/(1-x^9-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17-x^18).
%C A017885 Number of compositions (ordered partitions) of n into parts 9, 10, 11, 12, 13, 14, 15, 16, 17 and 18. - _Ilya Gutkovskiy_, May 27 2017
%H A017885 Vincenzo Librandi, <a href="/A017885/b017885.txt">Table of n, a(n) for n = 0..1000</a>
%H A017885 <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1).
%F A017885 a(n) = a(n-9) +a(n-10) +a(n-11) +a(n-12) +a(n-13) +a(n-14) +a(n-15) +a(n-16) +a(n-17) +a(n-18), for n>17. - _Vincenzo Librandi_, Jul 01 2013
%t A017885 CoefficientList[Series[1 / (1 - Total[x^Range[9, 18]]), {x, 0, 70}], x] (* _Vincenzo Librandi_, Jul 01 2013 *)
%o A017885 (Magma)
%o A017885 m:=70; R<x>:=PowerSeriesRing(Integers(), m);
%o A017885 Coefficients(R!(1/(1-x^9-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17-x^18))); // _Vincenzo Librandi_, Jul 01 2013
%o A017885 (SageMath)
%o A017885 def A017885_list(prec):
%o A017885     P.<x> = PowerSeriesRing(ZZ, prec)
%o A017885     return P( (1-x)/(1-x-x^9+x^(19)) ).list()
%o A017885 A017885_list(70) # _G. C. Greubel_, Sep 25 2024
%Y A017885 Cf. A017877, A017878, A017879, A017880, A017881, A017882, A017883, A017884, A017886.
%K A017885 nonn,easy
%O A017885 0,19
%A A017885 _N. J. A. Sloane_