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%I #17 Sep 08 2022 08:44:43
%S 1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,0,1,2,3,4,5,6,7,8,9,8,8,9,11,
%T 14,18,23,29,36,45,52,58,64,71,80,92,108,129,156,193,237,286,339,396,
%U 458,527,606,699,810,951,1130,1352
%N Expansion of 1/(1-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17-x^18).
%C Number of compositions (ordered partitions) of n into parts 10, 11, 12, 13, 14, 15, 16, 17 and 18. - _Ilya Gutkovskiy_, May 27 2017
%H Vincenzo Librandi, <a href="/A017894/b017894.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 (0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1).
%F a(n) = a(n-10) +a(n-11) +a(n-12) +a(n-13) +a(n-14) +a(n-15) +Self(n-16) +a(n-17) +a(n-18), for n>17. - _Vincenzo Librandi_, Jul 01 2013
%p a:= n-> (Matrix(18, (i, j)-> if (i=j-1) or (j=1 and i in [$10..18]) then 1 else 0 fi)^n)[1, 1]: seq(a(n), n=0..70); # _Alois P. Heinz_, Jul 01 2013
%t CoefficientList[Series[1 / (1 - Total[x^Range[10, 18]]), {x, 0, 70}], x] (* _Vincenzo Librandi_, Jul 01 2013 *)
%o (Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17-x^18))); /* or */ I:=[1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1]; [n le 18 select I[n] else Self(n-10)+Self(n-11)+Self(n-12)+Self(n-13)+Self(n-14)+Self(n-15)+Self(n-16)+Self(n-17)+Self(n-18): n in [1..70]]; // _Vincenzo Librandi_, Jul 01 2013
%K nonn,easy
%O 0,22
%A _N. J. A. Sloane_.
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