cp's OEIS Frontend

A017878 Expansion of 1/(1-x^9-x^10-x^11).

%I A017878 #22 Sep 25 2024 09:27:20
%S A017878 1,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,1,2,3,2,1,0,0,0,0,1,3,6,7,6,3,1,
%T A017878 0,0,1,4,10,16,19,16,10,4,1,1,5,15,30,45,51,45,30,15,6,7,21,50,90,126,
%U A017878 141,126,90,51,28,34,78,161
%N A017878 Expansion of 1/(1-x^9-x^10-x^11).
%C A017878 Number of compositions (ordered partitions) of n into parts 9, 10 and 11. - _Ilya Gutkovskiy_, May 27 2017
%H A017878 Vincenzo Librandi, <a href="/A017878/b017878.txt">Table of n, a(n) for n = 0..1000</a>
%H A017878 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,1,1,1).
%F A017878 a(n) = a(n-9) +a(n-10) +a(n-11) for n>10. - _Vincenzo Librandi_, Jul 01 2013
%t A017878 CoefficientList[Series[1 / (1 - Total[x^Range[9, 11]]), {x, 0, 80}], x] (* _Vincenzo Librandi_, Jul 01 2013 *)
%t A017878 LinearRecurrence[{0,0,0,0,0,0,0,0,1,1,1},{1,0,0,0,0,0,0,0,0,1,1},70] (* _Harvey P. Dale_, May 25 2023 *)
%o A017878 (Magma)
%o A017878 m:=70; R<x>:=PowerSeriesRing(Integers(), m);
%o A017878 Coefficients(R!(1/(1-x^9-x^10-x^11))); // _Vincenzo Librandi_, Jul 01 2013
%o A017878 (SageMath)
%o A017878 def A017878_list(prec):
%o A017878     P.<x> = PowerSeriesRing(ZZ, prec)
%o A017878     return P( (1-x)/(1-x-x^9+x^(12)) ).list()
%o A017878 A017878_list(80) # _G. C. Greubel_, Sep 25 2024
%Y A017878 Cf. A017877, A017879, A017880, A017881, A017882, A017883, A017884, A017885, A017886.
%K A017878 nonn,easy
%O A017878 0,20
%A A017878 _N. J. A. Sloane_