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%I #17 Sep 08 2022 08:44:43
%S 1,0,0,0,0,0,0,1,1,1,1,0,0,0,1,2,3,4,3,2,1,1,3,6,10,12,12,10,7,7,11,
%T 20,31,40,44,41,36,35,45,69,102,135,156,161,156,157,185,251,351,462,
%U 554,608,630,659,749,944,1249,1618
%N Expansion of 1/(1-x^7-x^8-x^9-x^10).
%C Number of compositions of n into parts p where 7 <= p <= 10. [_Joerg Arndt_, Jun 28 2013]
%H Vincenzo Librandi, <a href="/A017859/b017859.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).
%F a(n) = a(n-7) +a(n-8) +a(n-9) +a(n-10) for n>9. - _Vincenzo Librandi_, Jun 28 2013
%t CoefficientList[Series[1 / (1 - Total[x^Range[7, 10]]), {x, 0, 70}], x] (* _Vincenzo Librandi_, Jun 28 2013 *)
%t LinearRecurrence[{0,0,0,0,0,0,1,1,1,1},{1,0,0,0,0,0,0,1,1,1},60] (* _Harvey P. Dale_, Jun 21 2022 *)
%o (Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^7-x^8-x^9-x^10))); /* or */ I:=[1,0,0,0,0,0,0,1,1,1]; [n le 10 select I[n] else Self(n-7)+Self(n-8)+Self(n-9)+Self(n-10): n in [1..70]]; // _Vincenzo Librandi_, Jun 28 2013
%K nonn,easy
%O 0,16
%A _N. J. A. Sloane_.
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