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 A199579 #23 Sep 08 2022 08:46:00
%S A199579 1,4,28,232,2056,18784,174112,1625152,15220288,142777600,1340416768,
%T A199579 12588825088,118252556800,1110898849792,10436554713088,98050271875072,
%U A199579 921180638875648,8654518327066624,81309636020912128
%N A199579 Average number of round trips of length n on the Laguerre graph L_4.
%C A199579 See the general array and triangle for the average number of round trips of length L on (open) Laguerre graphs L_N given in A201198. Here a(n) = w(4,L=n), n>=0, the fourth row in this array. In the corresponding triangle this is the column no. N=4 without leading zeros: a(n) = A201198(n+3,4), n>=0.
%C A199579 For a sketch of this Laguerre graph L_4 see Figure 3 of the W. Lang link. The o.g.f. is also given there.
%C A199579 By definition the number of zero length round trips of length 0 for a vertex is put to 1 in order to count vertices.
%H A199579 G. C. Greubel, <a href="/A199579/b199579.txt">Table of n, a(n) for n = 0..450</a>
%H A199579 Wolfdieter Lang, <a href="/A201198/a201198_1.pdf">Counting walks on Jacobi graphs: an application of orthogonal polynomials.</a>
%H A199579 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (16,-72,96,-24)
%F A199579 a(n) = A201198(n+3,4), n>=0.
%F A199579 O.g.f.: (1-12*x+36*x^2-24*x^3)/(1-16*x+72*x^2-96*x^3+24*x^4).
%e A199579 n=0: a(0)=1 because the average number of vertices is 4/4=1.
%e A199579 a(1)= (1+3+5+7)/4 = 4, from the sum of the self-loops of L_4 divided by the number of vertices 4.
%e A199579 The counting for n=2, a(2)= 112/4 = 28, has been given as an example to A201198.
%t A199579 LinearRecurrence[{16, -72, 96, -24}, {1, 4, 28, 232}, 50] (* _G. C. Greubel_, May 14 2018 *)
%o A199579 (PARI) x='x+O('x^30); Vec((1-12*x+36*x^2-24*x^3)/(1-16*x+72*x^2- 96*x^3 +24*x^4)) \\ _G. C. Greubel_, May 14 2018
%o A199579 (Magma) I:=[1, 4, 28, 232]; [n le 4 select I[n] else 16*Self(n-1) - 72*Self(n-2) + 96*Self(n-3) -24*Self(n-4): n in [1..30]]; // _G. C. Greubel_, May 14 2018
%Y A199579 Cf. A201198, A201199 (closed Laguerre graphs), A201200 (closed L_4 graph).
%K A199579 nonn,easy,walk
%O A199579 0,2
%A A199579 _Wolfdieter Lang_, Dec 02 2011