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 A355480 #15 Jan 05 2023 16:11:17
%S A355480 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,
%T A355480 1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
%U A355480 2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3
%N A355480 a(n) is the number of distinct, hexagonal-tiled regions after the n-th step of the walk described in A355478.
%C A355480 See A355478 for additional information and animations.
%H A355480 Paolo Xausa, <a href="/A355480/b355480.txt">Table of n, a(n) for n = 0..9999</a>
%H A355480 Paolo Xausa, <a href="/A355480/a355480_1.pdf">Illustration of selected terms up to n = 11000</a>
%H A355480 <a href="/index/Wa#WALKS">Index entries for sequences related to walks</a>
%e A355480 In the following diagrams the walk is shown at the end of the n-th step, together with the position of the bee (*).
%e A355480 .
%e A355480 n 0 1 8 28 60
%e A355480 a(n) 0 0 0 1 2
%e A355480 __
%e A355480 __/ 2\*_
%e A355480 * __* __ __ / 2\__/ \__
%e A355480 \ \__ \__/ 2\__ \__
%e A355480 / / \__ \__/ 2\__/ \__
%e A355480 \ \*_ \__ \__/ \__ \__
%e A355480 / / 1\ \ / 1\ \
%e A355480 \ \__/ __/ \__/ __/
%e A355480 / / __/ / __/
%e A355480 \* \__/ \__/
%e A355480 .
%t A355480 A355480[nterms_]:=Module[{a={0},walk={{0,0}},angle=0,cells},Do[AppendTo[walk,AngleVector[Last[walk],angle+=If[PrimeQ[n],-1,1]Pi/3]];cells=FindCycle[Graph[MapApply[UndirectedEdge,Partition[walk,2,1]]],{6},All];AppendTo[a,Length[ConnectedComponents[Graph[Flatten[cells]]]]],{n,nterms-1}];Take[a,nterms]];
%t A355480 A355480[100]
%Y A355480 Cf. A174313, A211020, A233399, A355478, A355479.
%K A355480 nonn,walk
%O A355480 0,37
%A A355480 _Paolo Xausa_, Jul 21 2022