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A017896 Expansion of 1/(1-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17-x^18-x^19-x^20).

%I A017896 #27 Nov 08 2024 07:21:00
%S A017896 1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,3,4,5,6,7,8,9,10,12,13,
%T A017896 15,18,22,27,33,40,48,57,68,79,92,107,125,147,174,207,247,295,353,420,
%U A017896 499,591,698,823,970,1144,1351,1598,1894,2246,2666,3165,3756,4454,5277,6247,7391,8742,10341,12234
%N A017896 Expansion of 1/(1-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17-x^18-x^19-x^20).
%C A017896 Number of compositions (ordered partitions) of n into parts 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 and 20. - _Ilya Gutkovskiy_, May 27 2017
%H A017896 Vincenzo Librandi, <a href="/A017896/b017896.txt">Table of n, a(n) for n = 0..1000</a>
%H A017896 <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1).
%F A017896 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) +a(n-20), for n>19. - _Vincenzo Librandi_, Jul 01 2013
%p A017896 a:= n-> (Matrix(20, (i, j)-> if (i=j-1) or (j=1 and i in [$10..20]) then 1 else 0 fi)^n)[1, 1]: seq(a(n), n=0..80);  # _Alois P. Heinz_, Aug 04 2008
%t A017896 CoefficientList[Series[1/(1 -Total[x^Range[10, 20]]), {x,0,80}], x] (* _Vincenzo Librandi_, Jul 01 2013 *)
%t A017896 LinearRecurrence[{0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1},{1,0,0,0,0,0,0,0, 0,0,1,1,1,1,1,1,1,1,1,1}, 81] (* _Harvey P. Dale_, Oct 21 2016 *)
%o A017896 (Magma) R<x>:=PowerSeriesRing(Integers(), 80); Coefficients(R!(1/(1-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17-x^18-x^19-x^20))); // _Vincenzo Librandi_, Jul 01 2013
%o A017896 (SageMath)
%o A017896 def A017896_list(prec):
%o A017896     P.<x> = PowerSeriesRing(ZZ, prec)
%o A017896     return P( (1-x)/(1-x-x^10+x^21) ).list()
%o A017896 A017896_list(81) # _G. C. Greubel_, Nov 08 2024
%Y A017896 Cf. A017887.
%K A017896 nonn,easy
%O A017896 0,21
%A A017896 _N. J. A. Sloane_