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

%I #19 Mar 15 2023 14:47:11

%S 1,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,1,2,3,4,3,2,1,0,1,3,6,10,12,12,10,6,

%T 4,5,10,20,31,40,44,40,32,25,25,39,66,101,135,155,156,141,122,121,155,

%U 231,341,457,547,587,574,540

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

%C Number of compositions of n into parts p where 8 <= p <= 11. [_Joerg Arndt_, Jun 29 2013]

%H Vincenzo Librandi, <a href="/A017869/b017869.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,1,1,1,1).

%F G.f.: 1/(1-x^8-x^9-x^10-x^11).

%F a(n) = a(n-8) +a(n-9) +a(n-10) +a(n-11) for n>10. - _Vincenzo Librandi_, Jun 29 2013

%t CoefficientList[Series[1 / (1 - Total[x^Range[8, 11]]), {x, 0, 70}], x] (* _Vincenzo Librandi_, Jun 29 2013 *)

%t LinearRecurrence[{0,0,0,0,0,0,0,1,1,1,1},{1,0,0,0,0,0,0,0,1,1,1},60] (* _Harvey P. Dale_, Dec 31 2018 *)

%o (Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^8-x^9-x^10-x^11))); /* or */ I:=[1,0,0,0,0,0,0,0,1,1,1]; [n le 11 select I[n] else Self(n-8)+Self(n-9)+Self(n-10)+Self(n-11): n in [1..70]]; // _Vincenzo Librandi_, Jun 29 2013

%K nonn,easy

%O 0,18

%A _N. J. A. Sloane_.