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A355480
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a(n) is the number of distinct, hexagonal-tiled regions after the n-th step of the walk described in A355478.
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3
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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, 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, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3
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OFFSET
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0,37
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COMMENTS
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See A355478 for additional information and animations.
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LINKS
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EXAMPLE
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In the following diagrams the walk is shown at the end of the n-th step, together with the position of the bee (*).
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n 0 1 8 28 60
a(n) 0 0 0 1 2
__
__/ 2\*_
* __* __ __ / 2\__/ \__
\ \__ \__/ 2\__ \__
/ / \__ \__/ 2\__/ \__
\ \*_ \__ \__/ \__ \__
/ / 1\ \ / 1\ \
\ \__/ __/ \__/ __/
/ / __/ / __/
\* \__/ \__/
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MATHEMATICA
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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]];
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CROSSREFS
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KEYWORD
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nonn,walk
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AUTHOR
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STATUS
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approved
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