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 A201200 #25 Sep 08 2022 08:46:01
%S A201200 1,4,30,256,2356,22384,215640,2090176,20315536,197702464,1925042400,
%T A201200 18749072896,182629124416,1779030655744,17330352562560,
%U A201200 168824779580416,1644626142474496,16021353180980224,156074394613317120,1520422660926324736
%N A201200 Total number of round trips of length n on the closed Laguerre graph Lc_4 divided by 4.
%C A201200 For the general array and triangle for the total number of round trips of length L on closed Laguerre graphs Lc_N see A201199. Here a(n)=w(4,L=n)/4, n>=0, the fourth row of this array divided by 4. In the corresponding triangle a(n) = A201199(n+3,4)/4, n>=0.
%C A201200 For a sketch of the closed Laguerre graph Lc_4 see Figure 4 of the given W. Lang link. The o.g.f. is also found there.
%C A201200 By definition the number of length 0 round trips for a vertex is put to 1 in order to count vertices.
%C A201200 The average number of round trips of length n on a closed Laguerre graph Lc_N is in general a fraction. Therefore A201199 tabulates the total number of round trips.
%H A201200 Colin Barker, <a href="/A201200/b201200.txt">Table of n, a(n) for n = 0..1000</a>
%H A201200 Wolfdieter Lang, <a href="/A201198/a201198_1.pdf">Counting walks on Jacobi graphs: an application of orthogonal polynomials.</a>
%H A201200 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (16,-68,64,44).
%F A201200 a(n) = A201199(n+3,4)/4, n>=0.
%F A201200 O.g.f.: (8*x-1)*(2*x^2-4*x+1) / ( (22*x^2-12*x+1)*(2*x^2+4*x-1) ).
%F A201200 From _Colin Barker_, Apr 27 2016: (Start)
%F A201200 a(n) = 16*a(n-1)-68*a(n-2)+64*a(n-3)+44*a(n-4) for n>3.
%F A201200 a(n) = ((2-sqrt(6))^n+(2+sqrt(6))^n+(6-sqrt(14))^n+(6+sqrt(14))^n)/4.
%F A201200 (End)
%F A201200 E.g.f.: (exp((2-sqrt(6))*x) + exp((2+sqrt(6))*x) + exp((6-sqrt(14))*x) + exp((6+sqrt(14))*x))/4. - _Ilya Gutkovskiy_, Apr 27 2016
%t A201200 LinearRecurrence[{16,-68,64,44}, {1, 4, 30, 256}, 30] (* _G. C. Greubel_, May 13 2018 *)
%o A201200 (PARI) Vec((1-8*x)*(1-4*x+2*x^2)/((1-4*x-2*x^2)*(1-12*x+22*x^2)) + O(x^50)) \\ _Colin Barker_, Apr 27 2016
%o A201200 (Magma) I:=[1, 4, 30, 256]; [n le 4 select I[n] else 16*Self(n-1) - 68*Self(n-2) + 64*Self(n-3) + 44*Self(n-4): n in [1..30]]; // _G. C. Greubel_, May 13 2018
%Y A201200 Cf. A201199, A201198 (open Laguerre graphs). A199579 (open L_4 graph).
%K A201200 nonn,easy,walk
%O A201200 0,2
%A A201200 _Wolfdieter Lang_, Dec 02 2011
%E A201200 Typo in formula fixed by _Colin Barker_, Apr 27 2016