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A121364 Convolution of A066983 with the double Fibonacci sequence A103609.

%I A121364 #17 Oct 25 2024 09:33:15
%S A121364 0,0,1,2,3,6,10,18,29,50,81,136,220,364,589,966,1563,2550,4126,6710,
%T A121364 10857,17622,28513,46224,74792,121160,196041,317434,513619,831430,
%U A121364 1345282,2177322,3522981,5701290,9224881,14927768,24153636,39083988,63239221,102327390
%N A121364 Convolution of A066983 with the double Fibonacci sequence A103609.
%C A121364 The convolution of 1,0,1,1,1,3,3,7,9,17,25,... (A066983 with 1,0 added to the front) with "A double Fibonacci sequence" (A103609) is the Fibonacci sequence (A000045), with an extra initial 0.
%H A121364 G. C. Greubel, <a href="/A121364/b121364.txt">Table of n, a(n) for n = 1..1000</a>
%H A121364 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-1,0,-1,-1).
%F A121364 a(n) = F(n) - D(n+1), where F is the Fibonacci sequence (A000045) and D is "A double Fibonacci sequence" (A103609).
%F A121364 G.f.: x^3*(1+x-x^2) / ((1-x-x^2)*(1-x^2-x^4)). - _Colin Barker_, Oct 13 2014
%e A121364 a(7)=10 because F(7)=13 and D(8)=3 and a(7)=F(7)-D(8).
%t A121364 LinearRecurrence[{1,2,-1,0,-1,-1},{0, 0, 1, 2, 3, 6},40] (* _James C. McMahon_, Oct 17 2024 *)
%o A121364 (PARI) concat([0,0], Vec(-x^3*(x^2-x-1)/((x^2+x-1)*(x^4+x^2-1)) + O(x^100))) \\ _Colin Barker_, Oct 13 2014
%o A121364 (Magma)
%o A121364 A121364:= func< n | Fibonacci(n) - Fibonacci(Floor((n+1)/2)) >;
%o A121364 [A121364(n): n in [1..70]]; // _G. C. Greubel_, Oct 23 2024
%o A121364 (SageMath)
%o A121364 def A121364(n): return fibonacci(n) - fibonacci((n+1)//2)
%o A121364 [A121364(n) for n in range(1,71)] # _G. C. Greubel_, Oct 23 2024
%Y A121364 Cf. A000045, A066983, A103609.
%K A121364 nonn,easy
%O A121364 1,4
%A A121364 _Graeme McRae_, Jul 23 2006
%E A121364 More terms from _Colin Barker_, Oct 13 2014