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A017895 Expansion of 1/(1-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17-x^18-x^19).

%I A017895 #23 Apr 07 2025 10:34:17
%S A017895 1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,3,4,5,6,7,8,9,10,10,11,
%T A017895 13,16,20,25,31,38,46,55,64,73,83,95,110,129,153,183,220,265,319,381,
%U A017895 451,530,620,724,846,991,1165,1375,1630,1938,2306,2741,3251,3846,4539,5347,6292,7402,8713,10270
%N A017895 Expansion of 1/(1-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17-x^18-x^19).
%C A017895 Number of compositions (ordered partitions) of n into parts 10, 11, 12, 13, 14, 15, 16, 17, 18 and 19. - _Ilya Gutkovskiy_, May 27 2017
%H A017895 Vincenzo Librandi, <a href="/A017895/b017895.txt">Table of n, a(n) for n = 0..1000</a>
%H A017895 <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1).
%F A017895 a(n) = a(n-10) +a(n-11) +a(n-12) +a(n-13) +a(n-14) +a(n-15) +a(n-16) +a(n-17) +a(n-18) +a(n-19) for n>18. - _Vincenzo Librandi_, Jul 01 2013
%t A017895 CoefficientList[Series[1 / (1 - Total[x^Range[10, 19]]), {x, 0, 70}], x] (* _Vincenzo Librandi_ Jul 01 2013 *)
%t A017895 LinearRecurrence[{0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1},{1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1},80] (* _Harvey P. Dale_, Apr 07 2025 *)
%o A017895 (Magma)
%o A017895 R<x>:=PowerSeriesRing(Integers(), 80);
%o A017895 Coefficients(R!(1/(1-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17-x^18-x^19))); // _Vincenzo Librandi_, Jul 01 2013
%o A017895 (SageMath)
%o A017895 def A017895_list(prec):
%o A017895     P.<x> = PowerSeriesRing(ZZ, prec)
%o A017895     return P( (1-x)/(1-x-x^10+x^20) ).list()
%o A017895 A017895_list(81) # _G. C. Greubel_, Nov 08 2024
%Y A017895 Cf. A017887.
%K A017895 nonn,easy
%O A017895 0,22
%A A017895 _N. J. A. Sloane_