A355479 a(n) is the number of distinct honeycomb cell walls built after the n-th step of the walk described in A355478.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 20, 20, 20, 20, 21, 22, 23, 24, 24, 25, 26, 27, 28, 29, 30, 31, 31, 31, 31, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 40, 41, 42, 42, 43, 44, 45, 46, 46, 46, 47, 47, 48, 49, 50, 51, 51, 51

Offset

0,3

Comments

See A355478 for more information, animations, and illustration of selected terms.

Links

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

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      1      8        24               47
                                         __
                                      __/  \*_
      *      __*   __    __          /  \__/  \__
                     \     \__       \__/  \__   \__
                     /     /  \__       \__/  \__/  \__
                     \     \*_   \__       \__/  \__   \__
                     /     /  \     \            /  \     \
                     \     \__/   __/            \__/   __/
                     /     /   __/               /   __/
                     \*    \__/                  \__/
.

Mathematica

A355479[nmax_]:=Module[{a={0}, w={}, p1={0, 0}, p2, angle=0}, Do[w=Union[w, {Sort[{p1, p2=AngleVector[p1, angle+=If[PrimeQ[n], -1, 1]Pi/3]}]}]; p1=p2; AppendTo[a, Length[w]], {n, nmax}]; a];
A355479[100] (* Paolo Xausa, Jan 05 2023 *)

Crossrefs

Cf. A174313, A211020, A233399, A355478, A355480, A357434.

Sequence in context: A272215 A323366 A030066 * A192438 A081331 A369261

Adjacent sequences: A355476 A355477 A355478 * A355480 A355481 A355482

Keyword

nonn,walk

Author

Paolo Xausa, Jul 18 2022

Status

approved