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A017887 Expansion of 1/(1 - x^10 - x^11).

%I A017887 #38 Jul 16 2025 12:35:02
%S A017887 1,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,1,2,1,0,0,0,0,0,0,0,1,3,3,1,
%T A017887 0,0,0,0,0,0,1,4,6,4,1,0,0,0,0,0,1,5,10,10,5,1,0,0,0,0,1,6,15,20,15,6,
%U A017887 1,0,0,0,1,7,21,35,35,21,7,1
%N A017887 Expansion of 1/(1 - x^10 - x^11).
%C A017887 Number of compositions (ordered partitions) of n into parts 10 and 11. - _Ilya Gutkovskiy_, May 27 2017
%H A017887 Vincenzo Librandi, <a href="/A017887/b017887.txt">Table of n, a(n) for n = 0..1000</a>
%H A017887 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,1,1).
%F A017887 a(n) = a(n-10) + a(n-11) for n > 10. - _Vincenzo Librandi_, Jul 01 2013
%F A017887 a(n) = Sum_{k=0..floor(n/10)} binomial(k,n-10*k). - _Seiichi Manyama_, Oct 01 2024
%t A017887 CoefficientList[Series[1 / (1 - Total[x^Range[10, 11]]), {x, 0, 70}], x] (* _Vincenzo Librandi_, Jul 01 2013 *)
%t A017887 LinearRecurrence[{0,0,0,0,0,0,0,0,0,1,1},{1,0,0,0,0,0,0,0,0,0,1},100] (* _Harvey P. Dale_, Feb 04 2015 *)
%o A017887 (Magma) m:=80; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^10-x^11))); // _Vincenzo Librandi_, Jul 01 2013
%o A017887 (Magma) I:=[1,0,0,0,0,0,0,0,0,0,1]; [n le 11 select I[n] else Self(n-10)+Self(n-11): n in [1..80]]; // _Vincenzo Librandi_, Jul 01 2013
%o A017887 (SageMath)
%o A017887 def A017887_list(prec):
%o A017887     P.<x> = PowerSeriesRing(ZZ, prec)
%o A017887     return P( 1/(1-x^10-x^(11)) ).list()
%o A017887 A017887_list(100) # _G. C. Greubel_, Sep 25 2024
%Y A017887 Column k=10 of A306713.
%Y A017887 Cf. A017886, A017888, A017889, A017890, A017891, A017892, A017893, A017894, A017895, A017896.
%K A017887 nonn,easy
%O A017887 0,22
%A A017887 _N. J. A. Sloane_