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A017877 Expansion of 1/(1 - x^9 - x^10).

%I A017877 #38 Oct 01 2024 07:15:34
%S A017877 1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,1,2,1,0,0,0,0,0,0,1,3,3,1,0,0,0,
%T A017877 0,0,1,4,6,4,1,0,0,0,0,1,5,10,10,5,1,0,0,0,1,6,15,20,15,6,1,0,0,1,7,
%U A017877 21,35,35,21,7,1,0,1,8,28,56
%N A017877 Expansion of 1/(1 - x^9 - x^10).
%C A017877 Number of compositions (ordered partitions) of n into parts 9 and 10. - _Ilya Gutkovskiy_, May 27 2017
%H A017877 Vincenzo Librandi, <a href="/A017877/b017877.txt">Table of n, a(n) for n = 0..1000</a>
%H A017877 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,1,1).
%F A017877 a(n) = a(n-9) + a(n-10) for n > 9. - _Vincenzo Librandi_, Jul 01 2013
%F A017877 a(n) = Sum_{k=0..floor(n/9)} binomial(k,n-9*k). - _Seiichi Manyama_, Oct 01 2024
%t A017877 CoefficientList[Series[1 / (1 - Total[x^Range[9, 10]]), {x, 0, 80}], x] (* _Vincenzo Librandi_, Jul 01 2013 *)
%o A017877 (Magma)
%o A017877 m:=80; R<x>:=PowerSeriesRing(Integers(), m);
%o A017877 Coefficients(R!(1/(1-x^9-x^10))); // _Vincenzo Librandi_, Jul 01 2013
%o A017877 (SageMath)
%o A017877 def A017877_list(prec):
%o A017877     P.<x> = PowerSeriesRing(ZZ, prec)
%o A017877     return P( 1/(1-x^9-x^(10)) ).list()
%o A017877 A017877_list(85) # _G. C. Greubel_, Sep 25 2024
%Y A017877 Column k=9 of A306713.
%Y A017877 Cf. A017876, A017878, A017879, A017880, A017881, A017882, A017883, A017884, A017885, A017886.
%K A017877 nonn,easy
%O A017877 0,20
%A A017877 _N. J. A. Sloane_