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Expansion of 1/(1-x^10-x^11-x^12-x^13).
3

%I #22 Sep 26 2024 03:11:55

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

%T 12,12,10,6,3,1,1,4,10,20,31,40,44,40,31,20,11,9,16,35,65,101,135,155,

%U 155,135,102,71,56,71,125

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

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

%H Vincenzo Librandi, <a href="/A017889/b017889.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,1,1,1,1).

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

%t CoefficientList[Series[1 / (1 - Total[x^Range[10, 13]]), {x, 0, 80}], x] (* _Vincenzo Librandi_, Jul 01 2013 *)

%o (Magma)

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

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

%o (SageMath)

%o def A017889_list(prec):

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

%o return P( (1-x)/(1-x-x^10+x^(14)) ).list()

%o A017889_list(80) # _G. C. Greubel_, Sep 25 2024

%Y Cf. A017887, A017888, A017890, A017891, A017892, A017893, A017894, A017895, A017896.

%K nonn,easy

%O 0,22

%A _N. J. A. Sloane_