login
A355479
a(n) is the number of distinct honeycomb cell walls built after the n-th step of the walk described in A355478.
4
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.
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
KEYWORD
nonn,walk
AUTHOR
Paolo Xausa, Jul 18 2022
STATUS
approved