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 A318376 #37 Sep 02 2023 15:39:56
%S A318376 1,1,5,15,71,287,1237,5205,22105,93547,396419,1679019,7112825,
%T A318376 30129785,127632829,540659703,2290273903,9701751655,41097286445,
%U A318376 174090887853,737460853361,3123934276211,13233197998795,56056726205715,237460102927921,1005897137745457,4261048654187957
%N A318376 a(n) = F(n+1)^3 - 3*F(n-1)*F(n)^2, where F(n) = A000045(n), the n-th Fibonacci number.
%C A318376 a(n) is the number of Markov equivalence classes whose skeleton is a spider graph with three legs, each of which contains n nodes of degree at most two.
%C A318376 A001519 admits the related formula A001519(n) = F(n+1)^2 - 2*F(n-1)*F(n).
%H A318376 Colin Barker, <a href="/A318376/b318376.txt">Table of n, a(n) for n = 0..1000</a>
%H A318376 A. Radhakrishnan, L. Solus, and C. Uhler. <a href="https://arxiv.org/abs/1706.06091">Counting Markov equivalence classes for DAG models on trees</a>, arXiv:1706.06091 [math.CO], 2017; Discrete Applied Mathematics 244 (2018): 170-185.
%H A318376 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,6,-3,-1).
%F A318376 From _Colin Barker_, Aug 25 2018: (Start)
%F A318376 G.f.: (1 - 2 x - 4 x^2 - 3 x^3) / ((1 + x - x^2)*(1 - 4*x - x^2)).
%F A318376 a(n) = 3*a(n-1) + 6*a(n-2) - 3*a(n-3) - a(n-4) for n>3.
%F A318376 (End)
%t A318376 CoefficientList[Series[(1 - 2 x - 4 x^2 - 3 x^3) / ((1 + x - x^2) (1-4 x-x^2)), {x, 0, 26}], x] (* _Michael De Vlieger_, Aug 25 2018 *)
%t A318376 LinearRecurrence[{3, 6, -3, -1}, {1, 1, 5, 15, 71}, 26] (* _Stefano Spezia_, Sep 02 2018; a(0)=1 amended by _Georg Fischer_, Apr 03 2019 *)
%t A318376 Table[Fibonacci[n + 1]^3 - 3 Fibonacci[n-1] Fibonacci[n]^2, {n, 0, 25}] (* _Vincenzo Librandi_, Sep 03 2018 *)
%t A318376 #[[3]]^3-3#[[1]]#[[2]]^2&/@Partition[Fibonacci[Range[-1,30]],3,1] (* _Harvey P. Dale_, Sep 02 2023 *)
%o A318376 (PARI) a(n) = fibonacci(n+1)^3 - 3*fibonacci(n-1)*fibonacci(n)^2; \\ _Michel Marcus_, Aug 25 2018
%o A318376 (PARI) my(x='x+O('x^31)); Vec((1 - 2*x - 4*x^2 - 3*x^3) / ((1 + x - x^2)*(1 - 4*x - x^2))) \\ _Colin Barker_, Aug 25 2018 and Sep 06 2018
%o A318376 (Magma) [Fibonacci(n+1)^3 - 3*Fibonacci(n-1)*Fibonacci(n)^2: n in [1..30]]; // _Vincenzo Librandi_, Sep 03 2018
%Y A318376 Cf. A000045, A001519.
%K A318376 nonn,easy
%O A318376 0,3
%A A318376 _Liam Solus_, Aug 24 2018
%E A318376 a(0) = 1 inserted by _Vincenzo Librandi_, Sep 03 2018