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A017893 Expansion of 1/(1-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17).

%I A017893 #23 Dec 02 2024 13:20:37
%S A017893 1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,0,0,1,2,3,4,5,6,7,8,7,6,6,7,9,12,
%T A017893 16,21,28,36,42,46,49,52,56,62,71,84,105,135,171,210,250,290,330,371,
%U A017893 414,462,525,614,736,894,1088,1316,1575,1862,2171,2498,2852,3256,3742,4346,5104,6049,7210,8610
%N A017893 Expansion of 1/(1-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17).
%C A017893 Number of compositions (ordered partitions) of n into parts 10, 11, 12, 13, 14, 15, 16 and 17. - _Ilya Gutkovskiy_, May 27 2017
%H A017893 Vincenzo Librandi, <a href="/A017893/b017893.txt">Table of n, a(n) for n = 0..1000</a>
%H A017893 <a href="/index/Rec#order_17">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).
%F A017893 a(n) = a(n-10) +a(n-11) +a(n-12) +a(n-13) +a(n-14) +a(n-15) +a(n-16) +a(n-17), n>16. - _Vincenzo Librandi_, Jul 01 2013
%p A017893 a:= n-> (Matrix(17, (i, j)-> if (i=j-1) or (j=1 and i in [$10..17]) then 1 else 0 fi)^n)[1, 1]: seq(a(n), n=0..80);  # _Alois P. Heinz_, Jul 01 2013
%t A017893 CoefficientList[Series[1 / (1 - Total[x^Range[10, 17]]), {x, 0, 80}], x] (* _Vincenzo Librandi_, Jul 01 2013 *)
%t A017893 LinearRecurrence[{0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1},{1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1},80] (* _Harvey P. Dale_, Dec 02 2024 *)
%o A017893 (Magma)
%o A017893 R<x>:=PowerSeriesRing(Integers(), 80);
%o A017893 Coefficients(R!(1/(1-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17))); // _Vincenzo Librandi_, Jul 01 2013
%o A017893 (SageMath)
%o A017893 def A017893_list(prec):
%o A017893     P.<x> = PowerSeriesRing(ZZ, prec)
%o A017893     return P( (1-x)/(1-x-x^10+x^18) ).list()
%o A017893 A017893_list(80) # _G. C. Greubel_, Nov 06 2024
%Y A017893 Cf. A017887.
%K A017893 nonn,easy
%O A017893 0,22
%A A017893 _N. J. A. Sloane_