%I #20 May 29 2025 16:25:36

%S 1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,2,3,4,5,6,7,8,8,9,11,14,18,23,29,

%T 36,43,50,58,68,81,98,120,148,183,224,271,325,388,463,554,666,806,980,

%U 1193,1450,1757,2122,2556,3074

%N Expansion of 1/(1-x^8-x^9-x^10-x^11-x^12-x^13-x^14-x^15).

%C Number of compositions of n into parts p where 8 <= p <= 15. [_Joerg Arndt_, Jun 29 2013]

%H Vincenzo Librandi, <a href="/A017873/b017873.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 (0,0,0,0,0,0,0,1,1,1,1,1,1,1,1).

%F a(n) = a(n-8) +a(n-9) +a(n-10) +a(n-11) +a(n-12) +a(n-13) +a(n-14) +a(n-15) for n>14. - _Vincenzo Librandi_, Jun 29 2013

%t CoefficientList[Series[1 / (1 - Total[x^Range[8, 15]]), {x, 0, 70}], x] (* _Vincenzo Librandi_, Jun 29 2013 *)

%t LinearRecurrence[{0,0,0,0,0,0,0,1,1,1,1,1,1,1,1},{1,0,0,0,0,0,0,0,1,1,1,1,1,1,1},60] (* _Harvey P. Dale_, Dec 04 2019 *)

%o (Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^8-x^9-x^10-x^11-x^12-x^13-x^14-x^15))); // _Vincenzo Librandi_, Jun 29 2013

%o (Magma) I:=[1,0,0,0,0,0,0,0,1,1,1,1,1,1,1]; [n le 15 select I[n] else Self(n-8)+Self(n-9)+Self(n-10)+Self(n-11)+Self(n-12)+Self(n-13)+Self(n-14)+Self(n-15): n in [1..70]]; // _Vincenzo Librandi_, Jun 29 2013

%K nonn,easy

%O 0,18

%A _N. J. A. Sloane_