A017860 - OEIS

%I #18 Jun 03 2023 14:00:14

%S 1,0,0,0,0,0,0,1,1,1,1,1,0,0,1,2,3,4,5,4,3,3,4,6,10,15,18,19,19,19,20,

%T 26,38,53,68,81,90,95,103,122,156,205,266,330,387,437,491,566,681,852,

%U 1079,1344,1625,1911,2211,2562

%N Expansion of 1/(1-x^7-x^8-x^9-x^10-x^11).

%C Number of compositions of n into parts p where 7 <= p <= 11. [_Joerg Arndt_, Jun 28 2013]

%H Vincenzo Librandi, <a href="/A017860/b017860.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 (0,0,0,0,0,0,1,1,1,1,1).

%F a(n) = a(n-7) +a(n-8) +a(n-9) +a(n-10) +a(n-11) for n>10. - _Vincenzo Librandi_, Jun 28 2013

%t CoefficientList[Series[1 / (1 - Total[x^Range[7, 11]]), {x, 0, 70}], x] (* _Vincenzo Librandi_, Jun 28 2013 *)

%t LinearRecurrence[{0,0,0,0,0,0,1,1,1,1,1},{1,0,0,0,0,0,0,1,1,1,1},60] (* _Harvey P. Dale_, Jun 03 2023 *)

%o (Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^7-x^8-x^9-x^10-x^11))); /* or */ I:=[1,0,0,0,0,0,0,1,1,1,1]; [n le 11 select I[n] else Self(n-7)+Self(n-8)+Self(n-9)+Self(n-10)+Self(n-11): n in [1..70]]; // _Vincenzo Librandi_, Jun 28 2013

%K nonn,easy

%O 0,16

%A _N. J. A. Sloane_.