login
A355480
a(n) is the number of distinct, hexagonal-tiled regions after the n-th step of the walk described in A355478.
3
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
OFFSET
0,37
COMMENTS
See A355478 for additional information and animations.
EXAMPLE
In the following diagrams the walk is shown at the end of the n-th step, together with the position of the bee (*).
.
n 0 1 8 28 60
a(n) 0 0 0 1 2
__
__/ 2\*_
* __* __ __ / 2\__/ \__
\ \__ \__/ 2\__ \__
/ / \__ \__/ 2\__/ \__
\ \*_ \__ \__/ \__ \__
/ / 1\ \ / 1\ \
\ \__/ __/ \__/ __/
/ / __/ / __/
\* \__/ \__/
.
MATHEMATICA
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]];
A355480[100]
CROSSREFS
KEYWORD
nonn,walk
AUTHOR
Paolo Xausa, Jul 21 2022
STATUS
approved