This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A250102 #24 May 26 2020 10:49:49 %S A250102 0,16,64,16,2304,5776,7744,309136,451584,2062096,38837824,27920656, %T A250102 424030464,4570300816,1039933504,74815378576,501671890944,2396689936, %U A250102 11857885086784,50863084730896,8725926945024,1727825132557456,4673690093529664,5056176437385616,234290415599944704 %N A250102 a(n) = 2*5^n - (1+2i)^(2n) - (1-2i)^(2n) where i = sqrt(-1). %H A250102 Michael De Vlieger, <a href="/A250102/b250102.txt">Table of n, a(n) for n = 0..1430</a> %H A250102 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 A250102 Igor Pak, <a href="https://arxiv.org/abs/1803.06636">Complexity problems in enumerative combinatorics</a>, arXiv:1803.06636 [math.CO], 2018. %H A250102 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-1,5,125). %F A250102 From _Colin Barker_, Feb 20 2019: (Start) %F A250102 G.f.: 16*x*(1 + 5*x) / ((1 - 5*x)*(1 + 6*x + 25*x^2)). %F A250102 a(n) = -a(n-1) + 5*a(n-2) + 125*a(n-3) for n>2. %F A250102 (End) %t A250102 Array[2*5^# - (1 + 2 I)^(2 #) - (1 - 2 I)^(2 #) &, 25, 0] (* _Michael De Vlieger_, Jun 19 2018 *) %t A250102 LinearRecurrence[{-1,5,125},{0,16,64},30] (* _Harvey P. Dale_, May 26 2020 *) %o A250102 (PARI) a(n) = 2*5^n - (1+2*I)^(2*n) - (1-2*I)^(2*n) \\ _Michel Marcus_, Aug 28 2015 %o A250102 (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 A250102 Equals 16*A094423. %K A250102 nonn %O A250102 0,2 %A A250102 _N. J. A. Sloane_, Nov 15 2014