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%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_.
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