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%I #19 Sep 08 2022 08:44:43
%S 1,0,0,0,0,1,1,1,1,1,2,3,3,4,5,7,10,12,15,19,25,34,44,56,72,93,122,
%T 159,205,265,343,446,580,751,972,1259,1633,2120,2749,3562,4616,5984,
%U 7761,10064,13046,16911,21923,28425
%N Expansion of 1/(1-x^5-x^6-x^7-x^8-x^9-x^10-x^11).
%C Number of compositions of n into parts p where 5 <= p <= 11. [_Joerg Arndt_, Jun 27 2013]
%H Vincenzo Librandi, <a href="/A017842/b017842.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 (0,0,0,0,1,1,1,1,1,1,1).
%F a(n) = a(n-5) +a(n-6) +a(n-7) +a(n-8) +a(n-9) +a(n-10) +a(n-11) for n>10. - _Vincenzo Librandi_, Jun 27 2013
%t CoefficientList[Series[1 / (1 - Total[x^Range[5, 11]]), {x, 0, 50}], x] (* _Vincenzo Librandi_, Jun 27 2013 *)
%t LinearRecurrence[{0,0,0,0,1,1,1,1,1,1,1},{1,0,0,0,0,1,1,1,1,1,2},50] (* _Harvey P. Dale_, Feb 21 2022 *)
%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-x^11))); /* or */ I:=[1,0,0,0,0,1,1,1,1,1,2]; [n le 11 select I[n] else Self(n-5)+Self(n-6)+Self(n-7)+Self(n-8)+Self(n-9)+Self(n-10)+Self(n-11): n in [1..70]]; // _Vincenzo Librandi_, Jun 27 2013
%K nonn,easy
%O 0,11
%A _N. J. A. Sloane_.
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