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%I #24 May 26 2020 10:49:49
%S 0,16,64,16,2304,5776,7744,309136,451584,2062096,38837824,27920656,
%T 424030464,4570300816,1039933504,74815378576,501671890944,2396689936,
%U 11857885086784,50863084730896,8725926945024,1727825132557456,4673690093529664,5056176437385616,234290415599944704
%N a(n) = 2*5^n - (1+2i)^(2n) - (1-2i)^(2n) where i = sqrt(-1).
%H Michael De Vlieger, <a href="/A250102/b250102.txt">Table of n, a(n) for n = 0..1430</a>
%H Ira M. Gessel, <a href="http://people.brandeis.edu/~gessel/homepage/slides/nonneg.pdf">Rational Functions With Nonnegative Integer Coefficients</a>, slides, 50th Séminaire Lotharingien de Combinatoire, 2003.
%H Igor Pak, <a href="https://arxiv.org/abs/1803.06636">Complexity problems in enumerative combinatorics</a>, arXiv:1803.06636 [math.CO], 2018.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-1,5,125).
%F From _Colin Barker_, Feb 20 2019: (Start)
%F G.f.: 16*x*(1 + 5*x) / ((1 - 5*x)*(1 + 6*x + 25*x^2)).
%F a(n) = -a(n-1) + 5*a(n-2) + 125*a(n-3) for n>2.
%F (End)
%t Array[2*5^# - (1 + 2 I)^(2 #) - (1 - 2 I)^(2 #) &, 25, 0] (* _Michael De Vlieger_, Jun 19 2018 *)
%t LinearRecurrence[{-1,5,125},{0,16,64},30] (* _Harvey P. Dale_, May 26 2020 *)
%o (PARI) a(n) = 2*5^n - (1+2*I)^(2*n) - (1-2*I)^(2*n) \\ _Michel Marcus_, Aug 28 2015
%o (PARI) concat(0, Vec(16*x*(1 + 5*x) / ((1 - 5*x)*(1 + 6*x + 25*x^2)) + O(x^30))) \\ _Colin Barker_, Feb 20 2019
%Y Equals 16*A094423.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Nov 15 2014
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