%I #21 Sep 08 2022 08:44:43
%S 1,0,0,1,1,1,2,3,4,5,8,12,16,23,34,48,68,98,141,201,287,412,590,843,
%T 1207,1729,2474,3540,5068,7255,10383,14861,21273,30449,43581,62380,
%U 89289,127802,182927,261833,374774
%N Expansion of 1/(1-x^3-x^4-x^5-x^6-x^7-x^8).
%C Number of compositions (ordered partitions) of n into parts 3, 4, 5, 6, 7 and 8. - _Ilya Gutkovskiy_, May 25 2017
%H Vincenzo Librandi, <a href="/A017821/b017821.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 (0,0,1,1,1,1,1,1).
%F a(n) = a(n-3) +a(n-4) +a(n-5) +a(n-6) +a(n-7) +a(n-8) for n>7. - _Vincenzo Librandi_, Jun 27 2013
%t CoefficientList[Series[1 / (1 - Total[x^Range[3, 8]]), {x, 0, 50}], x] (* _Vincenzo Librandi_, Jun 27 2013 *)
%t LinearRecurrence[{0,0,1,1,1,1,1,1},{1,0,0,1,1,1,2,3},60] (* _Harvey P. Dale_, Mar 29 2022 *)
%o (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x^3-x^4-x^5-x^6-x^7-x^8)))); /* or */ I:=[1,0,0,1,1,1,2,3]; [n le 8 select I[n] else Self(n-3)+Self(n-4)+Self(n-5)+Self(n-6)+Self(n-7)+Self(n-8): n in [1..50]]; // _Vincenzo Librandi_, Jun 27 2013
%K nonn,easy
%O 0,7
%A _N. J. A. Sloane_.