A355480 a(n) is the number of distinct, hexagonal-tiled regions after the n-th step of the walk described in A355478.

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.

Links

Paolo Xausa, Table of n, a(n) for n = 0..9999

Paolo Xausa, Illustration of selected terms up to n = 11000

Index entries for sequences related to walks

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

Cf. A174313, A211020, A233399, A355478, A355479.

Sequence in context: A098391 A071702 A225541 * A076303 A339276 A343356

Adjacent sequences: A355477 A355478 A355479 * A355481 A355482 A355483

Keyword

nonn,walk

Author

Paolo Xausa, Jul 21 2022

Status

approved