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 A384605 #7 Jun 04 2025 23:21:59
%S A384605 1,2,6,12,32,68,172,380,932,2108,5076,11644,27732,64156,151796,352956,
%T A384605 831828,1940060,4561460,10658044,25023764,58533020,137311988,
%U A384605 321396540,753578452,1764540636,4136061364,9687067004,22702231188,53178376476,124613167220
%N A384605 Expansion of (1+x) / (1-x-4*x^2+2*x^3).
%C A384605 Number of walks of length n starting at vertex 2 in the following graph:
%C A384605 0 2
%C A384605 \ /|
%C A384605 1 |
%C A384605 / \|
%C A384605 4 3.
%H A384605 Sean A. Irvine, <a href="https://oeis.org/wiki/User:Sean_A._Irvine/Walks_on_Graphs#5_vertices">Walks on Graphs</a>.
%H A384605 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,4,-2).
%e A384605 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 A384605 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>>)[3,1]:
%p A384605 seq(a(n), n=0..32);
%t A384605 CoefficientList[Series[(1 + x)/(1 - x - 4*x^2 + 2*x^3), {x, 0, 32}], x]
%Y A384605 Cf. A384604 (vertices 0, 1, 4), A213173 (missing edge {2,3}), A382683 (missing edge {1,4}).
%K A384605 nonn,easy,walk
%O A384605 0,2
%A A384605 _Sean A. Irvine_, Jun 04 2025