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Sum_{i=0..3} binomial(Fibonacci(n),i).
1

%I #8 Dec 30 2023 16:53:40

%S 1,2,2,4,8,26,93,378,1562,6580,27776,117570,497785,2108418,8930754,

%T 37830676,160251624,678835194,2875587605,12181180442,51600296826,

%U 218582354212,925929680832,3922301042114,16615133763313

%N Sum_{i=0..3} binomial(Fibonacci(n),i).

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (5,0,-16,8,8,-3,-1).

%F G.f.: ( 1-3*x-8*x^2+10*x^3+12*x^4-6*x^5-2*x^6 ) / ( (x-1) *(x^2+4*x-1) *(x^2+x-1) *(x^2-x-1) ). - _R. J. Mathar_, May 08 2020

%p A032440 := proc(n)

%p add(binomial(combinat[fibonacci](n),i),i=0..3)

%p end proc:

%p seq(A032440(n),n=0..40) ; # _R. J. Mathar_, May 08 2020

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_