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Expansion of 1/(1-x^10-x^11-x^12-x^13-x^14-x^15).
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%I #25 Nov 06 2024 04:29:00

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

%T 15,21,25,27,27,25,22,19,20,26,38,57,80,104,125,140,147,145,140,139,

%U 150,182,240,325,430,544,653,741,801,836,861,903,996,1176,1466,1871,2374,2933,3494,4005,4436

%N Expansion of 1/(1-x^10-x^11-x^12-x^13-x^14-x^15).

%C Number of compositions (ordered partitions) of n into parts 10, 11, 12, 13, 14 and 15. - _Ilya Gutkovskiy_, May 27 2017

%H Vincenzo Librandi, <a href="/A017891/b017891.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_15">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).

%F a(n) = a(n-10) +a(n-11) +a(n-12) +a(n-13) +a(n-14) +a(n-15) for n>14. - _Vincenzo Librandi_, Jul 01 2013

%t CoefficientList[Series[1/(1 - Total[x^Range[10, 15]]), {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-x^15))); // _Vincenzo Librandi_, Jul 01 2013

%o (SageMath)

%o def A017891_list(prec):

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

%o return P( (1-x)/(1-x-x^10+x^16) ).list()

%o A017891_list(80) # _G. C. Greubel_, Nov 06 2024

%Y Cf. A017887.

%K nonn,easy

%O 0,22

%A _N. J. A. Sloane_