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A017883 Expansion of 1/(1-x^9-x^10-x^11-x^12-x^13-x^14-x^15-x^16).

%I A017883 #24 Sep 25 2024 09:27:29
%S A017883 1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,0,1,2,3,4,5,6,7,8,7,7,8,10,13,17,
%T A017883 22,28,36,42,47,52,58,66,77,92,112,141,176,215,257,302,351,406,470,
%U A017883 546,645,774,937,1136,1372,1646
%N A017883 Expansion of 1/(1-x^9-x^10-x^11-x^12-x^13-x^14-x^15-x^16).
%C A017883 Number of compositions (ordered partitions) of n into parts 9, 10, 11, 12, 13, 14, 15 and 16. - _Ilya Gutkovskiy_, May 27 2017
%H A017883 Vincenzo Librandi, <a href="/A017883/b017883.txt">Table of n, a(n) for n = 0..1000</a>
%H A017883 <a href="/index/Rec#order_16">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).
%F A017883 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) for n>15. - _Vincenzo Librandi_, Jul 01 2013
%t A017883 CoefficientList[Series[1 / (1 - Total[x^Range[9, 16]]), {x, 0, 70}], x] (* _Vincenzo Librandi_, Jul 01 2013 *)
%o A017883 (Magma)
%o A017883 m:=70; R<x>:=PowerSeriesRing(Integers(), m);
%o A017883 Coefficients(R!(1/(1-x^9-x^10-x^11-x^12-x^13-x^14-x^15-x^16))); // _Vincenzo Librandi_, Jul 01 2013
%o A017883 (SageMath)
%o A017883 def A017883_list(prec):
%o A017883     P.<x> = PowerSeriesRing(ZZ, prec)
%o A017883     return P( (1-x)/(1-x-x^9+x^(17)) ).list()
%o A017883 A017883_list(65) # _G. C. Greubel_, Sep 25 2024
%Y A017883 Cf. A017877, A017878, A017879, A017880, A017881, A017882, A017884, A017885, A017886.
%K A017883 nonn,easy
%O A017883 0,20
%A A017883 _N. J. A. Sloane_