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

Author

Paolo Xausa, Jul 21 2022

Keywords

• nonn
• walk

Comments

See A355478 for additional information and animations.

Examples

			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\     \
                     \     \__/   __/            \__/   __/
                     /     /   __/               /   __/
                     \*    \__/                  \__/
.
		

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

Crossrefs

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

Programs

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]