

A355479


a(n) is the number of distinct honeycomb cell walls built after the nth 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
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OFFSET

0,3


COMMENTS

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


LINKS



EXAMPLE

In the following diagrams the walk is shown at the end of the nth 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];


CROSSREFS



KEYWORD

nonn,walk


AUTHOR



STATUS

approved



