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A017889 Expansion of 1/(1-x^10-x^11-x^12-x^13).

%I A017889 #22 Sep 26 2024 03:11:55
%S A017889 1,0,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0,1,2,3,4,3,2,1,0,0,0,1,3,6,10,
%T A017889 12,12,10,6,3,1,1,4,10,20,31,40,44,40,31,20,11,9,16,35,65,101,135,155,
%U A017889 155,135,102,71,56,71,125
%N A017889 Expansion of 1/(1-x^10-x^11-x^12-x^13).
%C A017889 Number of compositions (ordered partitions) of n into parts 10, 11, 12 and 13. - _Ilya Gutkovskiy_, May 27 2017
%H A017889 Vincenzo Librandi, <a href="/A017889/b017889.txt">Table of n, a(n) for n = 0..1000</a>
%H A017889 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,1,1,1,1).
%F A017889 a(n) = a(n-10) +a(n-11) +a(n-12) +a(n-13) for n>12. - _Vincenzo Librandi_, Jul 01 2013
%t A017889 CoefficientList[Series[1 / (1 - Total[x^Range[10, 13]]), {x, 0, 80}], x] (* _Vincenzo Librandi_, Jul 01 2013 *)
%o A017889 (Magma)
%o A017889 m:=80; R<x>:=PowerSeriesRing(Integers(), m);
%o A017889 Coefficients(R!(1/(1-x^10-x^11-x^12-x^13))); // _Vincenzo Librandi_, Jul 01 2013
%o A017889 (SageMath)
%o A017889 def A017889_list(prec):
%o A017889     P.<x> = PowerSeriesRing(ZZ, prec)
%o A017889     return P( (1-x)/(1-x-x^10+x^(14)) ).list()
%o A017889 A017889_list(80) # _G. C. Greubel_, Sep 25 2024
%Y A017889 Cf. A017887, A017888, A017890, A017891, A017892, A017893, A017894, A017895, A017896.
%K A017889 nonn,easy
%O A017889 0,22
%A A017889 _N. J. A. Sloane_