A335381 - OEIS

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A335381

a(n) is the Y-coordinate of the n-th point of the Kochawave curve; sequence A335380 gives X-coordinates.

2

0, 0, 1, 0, 0, 1, 4, 2, 3, 2, 0, 1, 0, 0, 1, 0, 0, 1, 4, 2, 3, 6, 12, 9, 12, 10, 7, 8, 6, 7, 10, 8, 9, 8, 6, 7, 6, 4, 1, 2, 0, 1, 2, 2, 3, 2, 0, 1, 0, 0, 1, 0, 0, 1, 4, 2, 3, 2, 0, 1, 0, 0, 1, 0, 0, 1, 4, 2, 3, 6, 12, 9, 12, 10, 7, 8, 6, 7, 10, 8, 9, 12, 18

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,7

COMMENTS

Coordinates are given on a hexagonal lattice with X-axis and Y-axis as follows:

Y

/

/

0 ---- X

LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..4096

Rémy Sigrist, The Kochawave curve, a variant of the Koch curve, arXiv:2210.17320 [math.HO], 2022.

Rémy Sigrist, PARI program for A335381

Index entries for sequences related to coordinates of 2D curves

FORMULA

a(4^k) = 0 for any k >= 0.

EXAMPLE

The Kochawave curve starts (on a hexagonal lattice) as follows:

. . . . . . + . . .

/|6

/ |

/ |

. . . . . . | . .+ . .

/ | .../ 8

/ | ... /

/ | ... /

. . . . . . +. + . .

/ 7 |9

/ |

/ |

. . .+ . .+ . +11 | . .+ .

.../ 2 ... 5 / \ | .../ 14

... / ... / \ | ... /

... / ... / \| ... /

+-------+. +-------+. . . +-------+. +-------+

0 1 3 4 12 13 10 15 16

- hence a(2) = a(5) = a(11) = a(14) = 1.

PROG

(PARI) See Links section.

CROSSREFS

Sequence in context: A016513 A063447 A304786 * A018845 A333215 A028947

Adjacent sequences: A335378 A335379 A335380 * A335382 A335383 A335384

KEYWORD

nonn

AUTHOR

Rémy Sigrist, Jun 04 2020

STATUS

approved