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

%I #28 Sep 25 2024 16:15:18

%S 1,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,1,2,3,2,1,0,0,0,0,0,1,3,6,7,

%T 6,3,1,0,0,0,1,4,10,16,19,16,10,4,1,0,1,5,15,30,45,51,45,30,15,5,2,6,

%U 21,50,90,126,141,126,90,50

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

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

%H Vincenzo Librandi, <a href="/A017888/b017888.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,1,1,1).

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

%t CoefficientList[Series[1 / (1 - Total[x^Range[10, 12]]), {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))); // _Vincenzo Librandi_, Jul 01 2013

%o (PARI)

%o my(x='x+O('x^80)); Vec(1/(1-x^10-x^11-x^12)) \\ _Altug Alkan_, Oct 04 2018

%o (SageMath)

%o def A017888_list(prec):

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

%o return P( (1-x)/(1-x-x^10+x^(13)) ).list()

%o A017888_list(80) # _G. C. Greubel_, Sep 25 2024

%Y Cf. A017887, A017889, A017890, A017891, A017892, A017893, A017894, A017895, A017896.

%K nonn,easy

%O 0,22

%A _N. J. A. Sloane_