%I #16 Sep 08 2022 08:44:43
%S 1,0,0,0,0,0,1,1,1,1,1,1,1,2,3,4,5,6,6,7,9,12,16,21,26,31,37,45,56,71,
%T 91,115,143,176,216,266,331,415,521,652,812,1007,1247,1547,1925,2401,
%U 2997,3738,4654,5786,7190
%N Expansion of 1/(1-x^6-x^7-x^8-x^9-x^10-x^11).
%C Number of compositions of n into parts p where 6 <= p <= 11. [_Joerg Arndt_, Jun 28 2013]
%H Vincenzo Librandi, <a href="/A017851/b017851.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 (0,0,0,0,0,1,1,1,1,1,1).
%F a(n) = a(n-6) +a(n-7) +a(n-8) +a(n-9) +a(n-10) +a(n-11) for n>10. - _Vincenzo Librandi_, Jun 28 2013
%t CoefficientList[Series[1 / (1 - Total[x^Range[6, 11]]), {x, 0, 60}], x] (* _Vincenzo Librandi_, Jun 28 2013 *)
%o (Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^6-x^7-x^8-x^9-x^10-x^11))); /* or */ I:=[1,0,0,0,0,0,1,1,1,1,1]; [n le 11 select I[n] else Self(n-6)+Self(n-7)+Self(n-8)+Self(n-9)+Self(n-10)+Self(n-11): n in [1..70]]; // _Vincenzo Librandi_, Jun 28 2013
%K nonn,easy
%O 0,14
%A _N. J. A. Sloane_.