A017841 - OEIS

%I #19 Sep 08 2022 08:44:43

%S 1,0,0,0,0,1,1,1,1,1,2,2,3,4,5,7,8,10,13,17,23,29,37,47,60,78,100,129,

%T 166,213,274,351,451,580,746,960,1233,1584,2035,2615,3362,4321,5554,

%U 7138,9173,11789,15150,19471,25025

%N Expansion of 1/(1-x^5-x^6-x^7-x^8-x^9-x^10).

%C Number of compositions of n into parts p where 5 <= p <= 10. [_Joerg Arndt_, Jun 27 2013]

%H Vincenzo Librandi, <a href="/A017841/b017841.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,1,1,1,1,1,1).

%F a(n) = a(n-5)+a(n-6)+a(n-7)+a(n-8)+a(n-9)+a(n-10), for n>9. - _Vincenzo Librandi_, Jun 27 2013

%t CoefficientList[Series[1 / (1 - Total[x^Range[5, 10]]), {x, 0, 50}], x] (* _Vincenzo Librandi_, Jun 27 2013 *)

%t LinearRecurrence[{0, 0, 0, 0, 1, 1, 1, 1, 1, 1}, {1, 0, 0, 0, 0, 1, 1, 1, 1, 1}, 50] (* _Robert G. Wilson v_, Jun 27 2013 *)

%o (Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^5-x^6-x^7-x^8-x^9-x^10))); /* or */ I:=[1,0,0,0,0,1,1,1,1,1]; [n le 10 select I[n] else Self(n-5)+Self(n-6)+Self(n-7)+Self(n-8)+Self(n-9)+Self(n-10): n in [1..70]]; // _Vincenzo Librandi_, Jun 27 2013

%K nonn,easy

%O 0,11

%A _N. J. A. Sloane_.