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A017881 Expansion of 1/(1 - x^9 - x^10 - x^11 - x^12 - x^13 - x^14).

%I A017881 #26 Sep 25 2024 15:41:48
%S A017881 1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,0,0,0,1,2,3,4,5,6,5,4,3,3,4,6,10,15,21,
%T A017881 25,27,27,26,25,25,30,41,59,81,104,125,141,151,155,160,174,206,261,
%U A017881 340,440,551,661,757,836,906,987
%N A017881 Expansion of 1/(1 - x^9 - x^10 - x^11 - x^12 - x^13 - x^14).
%C A017881 Number of compositions (ordered partitions) of n into parts 9, 10, 11, 12, 13 and 14. - _Ilya Gutkovskiy_, May 27 2017
%H A017881 Vincenzo Librandi, <a href="/A017881/b017881.txt">Table of n, a(n) for n = 0..1000</a>
%H A017881 <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,1,1,1,1,1,1).
%F A017881 a(0)=1, a(1)=a(2)=a(3)=a(4)=a(5)=a(6)=a(7)=a(8)=0, a(9)=a(10)=a(11)=a(12)= a(13)=1, a(n) = a(n-9) + a(n-10) + a(n-11) + a(n-12) + a(n-13) + a(n-14). - _Harvey P. Dale_, Feb 27 2012
%t A017881 CoefficientList[Series[1/(1-Total[x^Range[9,14]]),{x,0,60}],x] (* or *) LinearRecurrence[{0,0,0,0,0,0,0,0,1,1,1,1,1,1},{1,0,0,0,0,0,0,0,0,1,1,1,1,1}, 60] (* _Harvey P. Dale_, Feb 27 2012 *)
%o A017881 (Magma)
%o A017881 R<x>:=PowerSeriesRing(Integers(), 80);
%o A017881 Coefficients(R!( (1-x)/(1-x-x^9+x^(15)) )); // _G. C. Greubel_, Sep 25 2024
%o A017881 (SageMath)
%o A017881 def A017881_list(prec):
%o A017881     P.<x> = PowerSeriesRing(ZZ, prec)
%o A017881     return P( (1-x)/(1-x-x^9+x^(15)) ).list()
%o A017881 A017881_list(80) # _G. C. Greubel_, Sep 25 2024
%Y A017881 Cf. A017877, A017878, A017879, A017880, A017882, A017883, A017884, A017885, A017886.
%K A017881 nonn,easy
%O A017881 0,20
%A A017881 _N. J. A. Sloane_