# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a144899
Showing 1-1 of 1

%I A144899 #12 Jul 28 2022 09:11:54
%S A144899 0,1,6,21,57,133,280,547,1010,1785,3047,5058,8208,13075,20513,31781,
%T A144899 48732,74090,111856,167903,250848,373330,553883,819681,1210561,
%U A144899 1784919,2628351,3866317,5682701,8347012,12254249,17983326,26382698,38695852,56745223,83201736
%N A144899 Expansion of x/((1-x-x^3)*(1-x)^5).
%H A144899 Vincenzo Librandi, <a href="/A144899/b144899.txt">Table of n, a(n) for n = 0..1000</a>
%H A144899 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,21,-20,16,-11,5,-1).
%F A144899 G.f.: x/((1-x-x^3)*(1-x)^5).
%F A144899 From _G. C. Greubel_, Jul 27 2022: (Start)
%F A144899 a(n) = Sum_{j=0..floor((n+4)/3)} binomial(n-2*j+4, j+5).
%F A144899 a(n) = A099567(n+4, 5). (End)
%p A144899 a:= n-> (Matrix(8, (i, j)-> if i=j-1 then 1 elif j=1 then [6, -15, 21, -20, 16, -11, 5, -1][i] else 0 fi)^n)[1, 2]: seq(a(n), n=0..40);
%t A144899 CoefficientList[Series[x/((1-x-x^3)(1-x)^5), {x, 0, 40}], x] (* _Vincenzo Librandi_, Jun 06 2013 *)
%o A144899 (Magma)
%o A144899 A144899:= func< n | n eq 0 select 0 else (&+[Binomial(n-2*j+4, j+5): j in [0..Floor((n+4)/3)]]) >;
%o A144899 [A144899(n): n in [0..40]]; // _G. C. Greubel_, Jul 27 2022
%o A144899 (SageMath)
%o A144899 def A144899(n): return sum(binomial(n-2*j+4, j+5) for j in (0..((n+4)//3)))
%o A144899 [A144899(n) for n in (0..40)] # _G. C. Greubel_, Jul 27 2022
%Y A144899 6th column of A144903.
%Y A144899 Cf. A000930, A050228, A077868, A144898, A144900, A144901, A144902, A144903, A144904, A226405.
%Y A144899 Cf. A078012, A099567, A135851.
%K A144899 nonn,easy
%O A144899 0,3
%A A144899 _Alois P. Heinz_, Sep 24 2008

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE