%I #18 Sep 08 2022 08:44:43
%S 1,0,0,0,0,0,1,1,1,1,1,0,1,2,3,4,5,4,4,5,7,10,15,18,20,22,25,30,41,55,
%T 70,85,100,115,138,173,221,281,351,425,508,611,747,928,1164,1451,1786,
%U 2176,2642,3219,3958,4901,6076
%N Expansion of 1/(1-x^6-x^7-x^8-x^9-x^10).
%C Number of compositions of n into parts p where 6 <= p <= 10. [_Joerg Arndt_, Jun 27 2013]
%H Vincenzo Librandi, <a href="/A017850/b017850.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 (0,0,0,0,0,1,1,1,1,1).
%F a(n) = a(n-6) +a(n-7) +a(n-8) +a(n-9) +a(n-10) for n>9. - _Vincenzo Librandi_, Jun 27 2013
%t CoefficientList[Series[1 / (1 - Total[x^Range[6, 10]]), {x, 0, 60}], x] (* _Vincenzo Librandi_, Jun 27 2013 *)
%t LinearRecurrence[{0,0,0,0,0,1,1,1,1,1},{1,0,0,0,0,0,1,1,1,1},60] (* _Harvey P. Dale_, Apr 28 2018 *)
%o (Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^6-x^7-x^8-x^9-x^10))); /* or */ I:=[1,0,0,0,0,0,1,1,1,1]; [n le 10 select I[n] else Self(n-6)+Self(n-7)+Self(n-8)+Self(n-9)+Self(n-10): n in [1..70]]; // _Vincenzo Librandi_, Jun 27 2013
%K nonn,easy
%O 0,14
%A _N. J. A. Sloane_.
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