%I #17 Sep 08 2022 08:44:43
%S 1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,2,3,4,5,6,7,7,8,10,13,17,22,28,34,40,
%T 47,56,68,84,105,132,164,201,244,295,357,434,532,656,810,998,1225,
%U 1498,1827,2227,2719,3328,4082,5012
%N Expansion of 1/(1-x^7-x^8-x^9-x^10-x^11-x^12-x^13).
%C Number of compositions of n into parts p where 7 <= p <= 13. [_Joerg Arndt_, Jun 28 2013]
%H Vincenzo Librandi, <a href="/A017862/b017862.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 (0,0,0,0,0,0,1,1,1,1,1,1,1).
%F a(n) = a(n-7) +a(n-8) +a(n-9) +a(n-10) +a(n-11) +a(n-12) +a(n-13) for n>12. - _Vincenzo Librandi_, Jun 28 2013
%t CoefficientList[Series[1 / (1 - Total[x^Range[7, 13]]), {x, 0, 70}], x] (* _Vincenzo Librandi_, Jun 28 2013 *)
%t LinearRecurrence[{0,0,0,0,0,0,1,1,1,1,1,1,1},{1,0,0,0,0,0,0,1,1,1,1,1,1},60] (* _Harvey P. Dale_, Feb 25 2018 *)
%o (Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^7-x^8-x^9-x^10-x^11-x^12-x^13))); /* or */ I:=[1,0,0,0,0,0,0,1,1,1,1,1,1 ]; [n le 13 select I[n] else Self(n-7)+Self(n-8)+Self(n-9)+Self(n-10)+Self(n-11)+Self(n-12)+Self(n-13): n in [1..70]]; // _Vincenzo Librandi_, Jun 28 2013
%K nonn,easy
%O 0,16
%A _N. J. A. Sloane_.