%I #16 May 09 2020 15:01:26
%S 1,2,2,4,8,31,163,1093,7547,52956,368831,2559196,17676661,121774888,
%T 837294004,5750356236,39462206694,270686172409,1856193470231,
%U 12726292640107,87243213304941,598041351085972
%N a(n) = Sum_{i=0..4} binomial(Fibonacci(n),i).
%H Robert Israel, <a href="/A032439/b032439.txt">Table of n, a(n) for n = 0..1198</a>
%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (11,-17,-124,276,396,-902,-462,946,220,-340,-44,39,3,-1).
%F G.f.: ( 1- 9*x -3*x^2 +140*x^3 -30*x^4 -689*x^5 +12*x^6 +1189*x^7 +129*x^8 -572*x^9 -46*x^10 +77*x^11 +5*x^12 -2*x^13 ) / ( (x-1) *(1+x) *(x^2+4*x-1) *(x^2-7*x+1) *(x^2+3*x+1) *(x^2-x-1) *(x^2-3*x+1) *(x^2+x-1) ). - _Robert Israel_, Mar 06 2019
%p ff:= unapply(expand(add(binomial(x,i),i=0..4)),x):
%p seq(ff(combinat:-fibonacci(n)),n=0..50); # _Robert Israel_, Mar 06 2019
%t LinearRecurrence[{11, -17, -124, 276, 396, -902, -462, 946, 220, -340, -44, 39, 3, -1}, {1, 2, 2, 4, 8, 31, 163, 1093, 7547, 52956, 368831, 2559196, 17676661, 121774888},50] (* _Georg Fischer_ May 09 2020 *)
%o (PARI) a(n) = my(fn=fibonacci(n)); sum(i=0, 4, binomial(fn,i)); \\ _Michel Marcus_, May 09 2020
%K nonn
%O 0,2
%A _N. J. A. Sloane_