%I #19 Sep 08 2022 08:44:43
%S 1,0,0,0,0,0,1,1,1,0,0,0,1,2,3,2,1,0,1,3,6,7,6,3,2,4,10,16,19,16,11,9,
%T 16,30,45,51,46,36,36,55,91,126,142,133,118,127,182,272,359,401,393,
%U 378,427,581,813,1032,1153,1172
%N Expansion of 1/(1-x^6-x^7-x^8).
%C Number of compositions of n into parts 6, 7, and 8. [_Joerg Arndt_, Jun 27 2013]
%H Vincenzo Librandi, <a href="/A017848/b017848.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 (0,0,0,0,0,1,1,1).
%F a(n) = a(n-6) +a(n-7) +a(n-8) for n>7. - _Vincenzo Librandi_, Jun 27 2013
%t CoefficientList[Series[1 / (1 - Total[x^Range[6, 8]]), {x, 0, 60}], x] (* _Vincenzo Librandi_, Jun 27 2013 *)
%o (Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^6-x^7-x^8))); /* or */ I:=[1,0,0,0,0,0,1,1]; [n le 8 select I[n] else Self(n-6)+Self(n-7)+Self(n-8): n in [1..70]]; // _Vincenzo Librandi_, Jun 27 2013
%K nonn,easy
%O 0,14
%A _N. J. A. Sloane_.
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