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A017894 Expansion of 1/(1-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17-x^18).

%I A017894 #21 Nov 07 2024 02:29:33
%S A017894 1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,0,1,2,3,4,5,6,7,8,9,8,8,9,11,
%T A017894 14,18,23,29,36,45,52,58,64,71,80,92,108,129,156,193,237,286,339,396,
%U A017894 458,527,606,699,810,951,1130,1352,1620,1936,2302,2721,3198,3741,4358,5072,5916,6929,8153,9631
%N A017894 Expansion of 1/(1-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17-x^18).
%C A017894 Number of compositions (ordered partitions) of n into parts 10, 11, 12, 13, 14, 15, 16, 17 and 18. - _Ilya Gutkovskiy_, May 27 2017
%H A017894 Vincenzo Librandi, <a href="/A017894/b017894.txt">Table of n, a(n) for n = 0..1000</a>
%H A017894 <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature  (0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1).
%F A017894 a(n) = a(n-10) +a(n-11) +a(n-12) +a(n-13) +a(n-14) +a(n-15) +Self(n-16) +a(n-17) +a(n-18), for n>17. - _Vincenzo Librandi_, Jul 01 2013
%p A017894 a:= n-> (Matrix(18, (i, j)-> if (i=j-1) or (j=1 and i in [$10..18]) then 1 else 0 fi)^n)[1, 1]: seq(a(n), n=0..80);  # _Alois P. Heinz_, Jul 01 2013
%t A017894 CoefficientList[Series[1 / (1 - Total[x^Range[10, 18]]), {x, 0, 80}], x] (* _Vincenzo Librandi_, Jul 01 2013 *)
%o A017894 (Magma)
%o A017894 R<x>:=PowerSeriesRing(Integers(), 80);
%o A017894 Coefficients(R!(1/(1-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17-x^18))); // _Vincenzo Librandi_, Jul 01 2013
%o A017894 (SageMath)
%o A017894 def A017894_list(prec):
%o A017894     P.<x> = PowerSeriesRing(ZZ, prec)
%o A017894     return P( (1-x)/(1-x-x^10+x^19) ).list()
%o A017894 A017894_list(80) # _G. C. Greubel_, Nov 06 2024
%Y A017894 Cf. A017887.
%K A017894 nonn,easy
%O A017894 0,22
%A A017894 _N. J. A. Sloane_