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%I #18 Sep 08 2022 08:44:43
%S 1,0,0,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,1,2,3,4,5,4,3,2,1,1,3,6,10,15,18,
%T 19,18,15,11,10,13,21,35,52,68,80,85,81,73,67,70,90,131,189,256,320,
%U 366,387,386,376,381,431,547
%N Expansion of 1/(1-x^9-x^10-x^11-x^12-x^13).
%C Number of compositions (ordered partitions) of n into parts 9, 10, 11, 12 and 13. - _Ilya Gutkovskiy_, May 27 2017
%H Vincenzo Librandi, <a href="/A017880/b017880.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).
%F a(n) = a(n-9) +a(n-10) +a(n-11) +a(n-12) +a(n-13) for n>12. - _Vincenzo Librandi_, Jul 01 2013
%t CoefficientList[Series[1 / (1 - Total[x^Range[9, 13]]), {x, 0, 80}], x] (* _Vincenzo Librandi_, Jul 01 2013 *)
%t LinearRecurrence[{0,0,0,0,0,0,0,0,1,1,1,1,1},{1,0,0,0,0,0,0,0,0,1,1,1,1},70] (* _Harvey P. Dale_, Apr 03 2018 *)
%o (Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^9-x^10-x^11-x^12-x^13))); /* or */ I:=[1,0,0,0,0,0,0,0,0,1,1,1,1]; [n le 13 select I[n] else Self(n-9)+Self(n-10)+Self(n-11)+Self(n-12)+Self(n-13): n in [1..70]]; // _Vincenzo Librandi_, Jul 01 2013
%K nonn,easy
%O 0,20
%A _N. J. A. Sloane_.
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