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A121364 Convolution of A066983 with the double Fibonacci sequence A103609. 0


%S 0,0,1,2,3,6,10,18,29,50,81,136,220,364,589,966,1563,2550,4126,6710,

%T 10857,17622,28513,46224,74792,121160,196041,317434,513619,831430,

%U 1345282,2177322,3522981,5701290,9224881,14927768,24153636,39083988,63239221,102327390

%N Convolution of A066983 with the double Fibonacci sequence A103609.

%C 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 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-1,0,-1,-1).

%F a(n) = F(n) - D(n+1), where F is the Fibonacci sequence (A000045) and D is "A double Fibonacci sequence" (A103609).

%F G.f.: -x^3*(x^2-x-1) / ((x^2+x-1)*(x^4+x^2-1)). - _Colin Barker_, Oct 13 2014

%e a(7)=10 because F(7)=13 and D(8)=3 and a(7)=F(7)-D(8).

%o (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

%Y Cf. A066983, A103609, A000045.

%K nonn,easy

%O 1,4

%A _Graeme McRae_, Jul 23 2006

%E More terms from _Colin Barker_, Oct 13 2014

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Last modified May 9 03:06 EDT 2021. Contains 343685 sequences. (Running on oeis4.)