A017839 - OEIS

%I #18 Sep 08 2022 08:44:43

%S 1,0,0,0,0,1,1,1,1,0,1,2,3,4,3,3,4,6,10,12,13,14,16,23,32,41,49,55,66,

%T 85,112,145,177,211,255,318,408,519,645,788,961,1192,1500,1890,2360,

%U 2913,3586,4441,5543,6942,8663

%N Expansion of 1/(1-x^5-x^6-x^7-x^8).

%C Number of compositions of n into parts p where 5 <= p <= 8. [_Joerg Arndt_, Jun 27 2013]

%H Vincenzo Librandi, <a href="/A017839/b017839.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 (0,0,0,0,1,1,1,1).

%F a(a) = 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[5, 8]]), {x, 0, 50}], x] (* _Vincenzo Librandi_, Jun 27 2013 *)

%t LinearRecurrence[{0,0,0,0,1,1,1,1},{1,0,0,0,0,1,1,1},60] (* _Harvey P. Dale_, Jan 18 2015 *)

%o (Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^5-x^6-x^7-x^8))); /* or */ I:=[1,0,0,0,0,1,1,1]; [n le 8 select I[n] else Self(n-5)+Self(n-6)+Self(n-7)+Self(n-8): n in [1..70]]; // _Vincenzo Librandi_, Jun 27 2013

%K nonn,easy

%O 0,12

%A _N. J. A. Sloane_.