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 A355480 a(n) is the number of distinct, hexagonal-tiled regions after the n-th step of the walk described in A355478. 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,37 COMMENTS See A355478 for additional information and animations. 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 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 0 0 1 2 __ __/ 2\*_ * __* __ __ / 2\__/ \__ \ \__ \__/ 2\__ \__ / / \__ \__/ 2\__/ \__ \ \*_ \__ \__/ \__ \__ / / 1\ \ / 1\ \ \ \__/ __/ \__/ __/ / / __/ / __/ \* \__/ \__/ . 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] CROSSREFS Cf. A174313, A211020, A233399, A355478, A355479. Sequence in context: A098391 A071702 A225541 * A076303 A339276 A343356 Adjacent sequences: A355477 A355478 A355479 * A355481 A355482 A355483 KEYWORD nonn,walk AUTHOR Paolo Xausa, Jul 21 2022 STATUS approved

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Last modified December 9 23:06 EST 2023. Contains 367696 sequences. (Running on oeis4.)