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%I #17 Sep 20 2023 12:35:01
%S 1,0,0,0,0,1,1,1,1,1,2,3,4,5,6,8,10,14,19,25,33,42,55,73,97,129,169,
%T 221,290,382,505,666,877,1153,1516,1996,2629,3464,4562,6005,7904,
%U 10404,13699,18040,23755,31277,41176
%N Expansion of 1/(1-x^5-x^6-x^7-x^8-x^9-x^10-x^11-x^12-x^13-x^14-x^15).
%C Number of compositions of n into parts p where 5 <= p <= 15. [_Joerg Arndt_, Jun 27 2013]
%H Vincenzo Librandi, <a href="/A017846/b017846.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 (0,0,0,0,1,1,1,1,1,1,1,1,1,1,1).
%F a(n) = a(n-5) +a(n-6) +a(n-7) +a(n-8) +a(n-9) +a(n-10) +a(n-11) +a(n-12) +a(n-13) +a(n-14) +a(n-15) for n>14. - _Vincenzo Librandi_, Jun 27 2013
%t CoefficientList[Series[1 / (1 - Total[x^Range[5, 15]]), {x, 0, 50}], x] (* _Vincenzo Librandi_, Jun 27 2013 *)
%t LinearRecurrence[{0,0,0,0,1,1,1,1,1,1,1,1,1,1,1},{1,0,0,0,0,1,1,1,1,1,2,3,4,5,6},50] (* _Harvey P. Dale_, Sep 20 2023 *)
%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-x^12-x^13-x^14-x^15))); /* or */ I:=[1,0,0,0,0,1,1,1,1,1,2,3,4,5,6]; [n le 15 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)+Self(n-12)+Self(n-13)+Self(n-14)+Self(n-15): n in [1..70]]; // _Vincenzo Librandi_, Jun 27 2013
%K nonn,easy
%O 0,11
%A _N. J. A. Sloane_.
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