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%I #20 Sep 08 2022 08:44:43
%S 1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,3,4,5,6,7,8,9,9,10,12,15,19,
%T 24,30,37,45,53,61,70,81,95,113,136,165,201,245,296,354,420,496,585,
%U 691,819,975,1167,1402,1686,2025
%N Expansion of 1/(1-x^9-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17).
%C Number of compositions (ordered partitions) of n into parts 9, 10, 11, 12, 13, 14, 15, 16 and 17. - _Ilya Gutkovskiy_, May 27 2017
%H Vincenzo Librandi, <a href="/A017884/b017884.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1).
%F a(n) = a(n-9) +a(n-10) +a(n-11) +a(n-12) +a(n-13) +a(n-14) +a(n-15) +a(n-16) +a(n-17) for n>16. - _Vincenzo Librandi_, Jul 01 2013
%t CoefficientList[Series[1 / (1 - Total[x^Range[9, 17]]), {x, 0, 60}], x] (* _Harvey P. Dale_, Sep 12 2012 *)
%o (Magma) I:=[1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1]; [n le 17 select I[n] else Self(n-9)+Self(n-10)+Self(n-11)+Self(n-12)+Self(n-13)+Self(n-14)+Self(n-15)+Self(n-16)+Self(n-17): n in [1..70]]; /* or */ m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^9-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17))); // _Vincenzo Librandi_, Jul 01 2013
%K nonn,easy
%O 0,20
%A _N. J. A. Sloane_.
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