%I #19 Sep 08 2022 08:44:43
%S 1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,2,2,3,4,5,6,7,8,10,11,13,16,20,25,31,
%T 38,47,56,67,80,96,116,141,172,211,257,313,380,460,556,672,813,986,
%U 1196,1453,1766,2146,2606,3162
%N Expansion of 1/(1-x^8-x^9-x^10-x^11-x^12-x^13-x^14-x^15-x^16).
%C Number of compositions of n into parts p where 8 <= p <= 16. [_Joerg Arndt_, Jun 29 2013]
%H Vincenzo Librandi, <a href="/A017874/b017874.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1).
%F G.f.: 1/(1-x^8-x^9-x^10-x^11-x^12-x^13-x^14-x^15-x^16).
%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) +a(n-16) for n>15. - _Vincenzo Librandi_, Jun 29 2013
%t CoefficientList[Series[1 / (1 - Total[x^Range[8, 16]]), {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},{1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1},60] (* _Harvey P. Dale_, Dec 05 2015 *)
%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-x^16))); /* or */ I:=[1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1]; [n le 16 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)+Self(n-16): n in [1..70]]; // _Vincenzo Librandi_, Jun 29 2013
%K nonn,easy
%O 0,17
%A _N. J. A. Sloane_