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 A384604 #7 Jun 04 2025 23:22:04
%S A384604 1,1,4,6,20,36,104,208,552,1176,2968,6568,16088,36424,87640,201160,
%T A384604 478872,1108232,2621400,6096584,14365720,33509256,78778968,184084552,
%U A384604 432181912,1010962184,2371520728,5551005640,13015164184,30476145288,71434790744,167309043528
%N A384604 Expansion of (1-x^2) / (1-x-4*x^2+2*x^3).
%C A384604 Number of walks of length n starting at vertex 0 in the following graph:
%C A384604 0 2
%C A384604 \ /|
%C A384604 1 |
%C A384604 / \|
%C A384604 4 3.
%C A384604 Also, for n >= 1, the number of walks of length n-1 starting at vertex 1 in the same graph.
%H A384604 Sean A. Irvine, <a href="https://oeis.org/wiki/User:Sean_A._Irvine/Walks_on_Graphs#5_vertices">Walks on Graphs</a>.
%H A384604 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,4,-2).
%e A384604 a(3)=6 because we have the walks 0-1-0-1, 0-1-2-1, 0-1-2-3, 0-1-3-1, 0-1-3-2, 0-1-4-1.
%p A384604 a:= n-> (<<0|1|0|0|0>, <1|0|1|1|1>, <0|1|0|1|0>, <0|1|1|0|0>, <0|1|0|0|0>>^n. <<1,1,1,1,1>>)[1,1]:
%p A384604 seq(a(n), n=0..32);
%t A384604 CoefficientList[Series[(1 - x^2)/(1 - x - 4*x^2 + 2*x^3), {x, 0, 32}], x]
%Y A384604 Cf. A384605 (vertex 2), A213173 (missing edge {2,3}), A382683 (missing edge {1,4}).
%K A384604 nonn,easy,walk
%O A384604 0,3
%A A384604 _Sean A. Irvine_, Jun 04 2025