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Expansion of 1/(1-x^10-x^11-x^12-x^13-x^14).
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%I #23 Nov 06 2024 04:29:52

%S 1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,2,3,4,5,4,3,2,1,0,1,3,6,10,

%T 15,18,19,18,15,10,7,7,11,20,35,52,68,80,85,80,69,57,50,55,80,125,186,

%U 255,320,365,382,371,341,311,311,367,496,701,966,1251,1508,1693,1779,1770,1716,1701,1826

%N Expansion of 1/(1-x^10-x^11-x^12-x^13-x^14).

%C Number of compositions (ordered partitions) of n into parts 10, 11, 12, 13 and 14. - _Ilya Gutkovskiy_, May 27 2017

%H Vincenzo Librandi, <a href="/A017890/b017890.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,1,1,1,1,1).

%F a(n) = a(n-10) +a(n-11) +a(n-12) +a(n-13) +a(n-14) for n>13. - _Vincenzo Librandi_, Jul 01 2013

%t CoefficientList[Series[1 / (1 - Total[x^Range[10, 14]]), {x, 0, 80}], x] (* _Vincenzo Librandi_, Jul 01 2013 *)

%o (Magma)

%o R<x>:=PowerSeriesRing(Integers(), 80);

%o Coefficients(R!(1/(1-x^10-x^11-x^12-x^13-x^14))); // _Vincenzo Librandi_, Jul 01 2013

%o (SageMath)

%o def A017890_list(prec):

%o P.<x> = PowerSeriesRing(ZZ, prec)

%o return P( (1-x)/(1-x-x^10+x^15) ).list()

%o A017890_list(80) # _G. C. Greubel_, Nov 06 2024

%Y Cf. A017887.

%K nonn,easy,changed

%O 0,22

%A _N. J. A. Sloane_