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%I A017870 #18 Dec 31 2023 13:14:07
%S A017870 1,0,0,0,0,0,0,0,1,1,1,1,1,0,0,0,1,2,3,4,5,4,3,2,2,3,6,10,15,18,19,18,
%T A017870 16,14,16,23,36,52,68,80,86,85,83,87,105,141,195,259,322,371,402,421,
%U A017870 446,501,611,787,1022,1288
%N A017870 Expansion of 1/(1-x^8-x^9-x^10-x^11-x^12).
%C A017870 Number of compositions of n into parts p where 8 <= p <= 12. [_Joerg Arndt_, Jun 29 2013]
%H A017870 Harvey P. Dale, <a href="/A017870/b017870.txt">Table of n, a(n) for n = 0..1000</a>
%H A017870 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,1,1,1,1,1).
%F A017870 a(n) = a(n-8) +a(n-9) +a(n-10) +a(n-11) +a(n-12) for n>11. - _Vincenzo Librandi_, Jun 29 2013
%t A017870 CoefficientList[Series[1 / (1 - Total[x^Range[8, 12]]), {x, 0, 70}], x] (* _Vincenzo Librandi_, Jun 29 2013 *)
%t A017870 LinearRecurrence[{0,0,0,0,0,0,0,1,1,1,1,1},{1,0,0,0,0,0,0,0,1,1,1,1},60] (* _Harvey P. Dale_, Dec 31 2023 *)
%o A017870 (Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^8-x^9-x^10-x^11-x^12))); /* or */ I:=[1,0,0,0,0,0,0,0,1,1,1,1]; [n le 12 select I[n] else Self(n-8)+Self(n-9)+Self(n-10)+Self(n-11)+Self(n-12): n in [1..70]]; // _Vincenzo Librandi_, Jun 29 2013
%K A017870 nonn,easy
%O A017870 0,18
%A A017870 _N. J. A. Sloane_.

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