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A017884 Expansion of 1/(1-x^9-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17).

%I A017884 #23 Sep 25 2024 15:47:52
%S A017884 1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,3,4,5,6,7,8,9,9,10,12,15,19,
%T A017884 24,30,37,45,53,61,70,81,95,113,136,165,201,245,296,354,420,496,585,
%U A017884 691,819,975,1167,1402,1686,2025
%N A017884 Expansion of 1/(1-x^9-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17).
%C A017884 Number of compositions (ordered partitions) of n into parts 9, 10, 11, 12, 13, 14, 15, 16 and 17. - _Ilya Gutkovskiy_, May 27 2017
%H A017884 Vincenzo Librandi, <a href="/A017884/b017884.txt">Table of n, a(n) for n = 0..1000</a>
%H A017884 <a href="/index/Rec#order_17">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).
%F A017884 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) for n>16. - _Vincenzo Librandi_, Jul 01 2013
%t A017884 CoefficientList[Series[1 / (1 - Total[x^Range[9, 17]]), {x, 0, 60}], x] (* _Harvey P. Dale_, Sep 12 2012 *)
%o A017884 (Magma)
%o A017884 m:=70; R<x>:=PowerSeriesRing(Integers(), m);
%o A017884 Coefficients(R!(1/(1-x^9-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17))); // _Vincenzo Librandi_, Jul 01 2013
%o A017884 (SageMath)
%o A017884 def A017884_list(prec):
%o A017884     P.<x> = PowerSeriesRing(ZZ, prec)
%o A017884     return P( (1-x)/(1-x-x^9+x^(18)) ).list()
%o A017884 A017884_list(70) # _G. C. Greubel_, Sep 25 2024
%Y A017884 Cf. A017877, A017878, A017879, A017880, A017881, A017882, A017883, A017885, A017886.
%K A017884 nonn,easy
%O A017884 0,20
%A A017884 _N. J. A. Sloane_