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

Author

Paolo Xausa, Jul 18 2022

Keywords

• nonn
• walk

Comments

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

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

Links

• Paolo Xausa, Table of n, a(n) for n = 0..9999
• Index entries for sequences related to walks

Crossrefs

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

Programs

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 *)