%I #21 Sep 08 2022 08:44:43
%S 1,0,0,1,1,1,2,3,4,6,9,13,18,27,40,57,83,122,177,257,375,546,794,1156,
%T 1684,2451,3567,5194,7562,11007,16024,23329,33961,49439,71974,104779,
%U 152534,222057,323269,470609,685104
%N Expansion of 1/(1-x^3-x^4-x^5-x^6-x^7-x^8-x^9-x^10-x^11).
%C Number of compositions of n into parts p where 3 <= p <= 11. [_Joerg Arndt_, Jun 27 2013]
%H Vincenzo Librandi, <a href="/A017824/b017824.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 (0,0,1,1,1,1,1,1,1,1,1).
%F a(0)=1, a(1)=0, a(2)=0, a(3)=1, a(4)=1, a(5)=1, a(6)=2, a(7)=3, a(8)=4, a(9)=6, a(10)=9; for n>10, a(n) = a(n-3) +a(n-4) +a(n-5) +a(n-6) +a(n-7) +a(n-8) +a(n-9) +a(n-10) +a(n-11). - _Harvey P. Dale_, Sep 07 2012
%t CoefficientList[Series[1/(1 - Total[x^Range[3, 11]]), {x, 0, 40}], x] (* or *) LinearRecurrence[ {0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1},{1, 0, 0, 1, 1, 1, 2, 3, 4, 6, 9}, 41] (* _Harvey P. Dale_, Sep 07 2012 *)
%o (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^3-x^4-x^5-x^6-x^7-x^8-x^9-x^10-x^11))); /* or */ I:=[1,0,0,1,1,1,2,3,4,6,9]; [n le 11 select I[n] else Self(n-3)+Self(n-4)+Self(n-5)+Self(n-6)+Self(n-7)+Self(n-8)+Self(n-9)+Self(n-10)+Self(n-11): n in [1..50]]; // _Vincenzo Librandi_, Jun 27 2013
%K nonn,easy
%O 0,7
%A _N. J. A. Sloane_.
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