A339456 a(n) is the Y-coordinate of the n-th point of the space filling curve H defined in Comments section; A339455 gives X-coordinates.

0, 0, 1, 1, 0, -1, -1, 0, 0, 1, 2, 2, 3, 3, 2, 1, 1, 2, 2, 1, 0, -1, -2, -2, -1, -1, -2, -3, -3, -2, -2, -1, 0, 0, 1, 1, 0, -1, -1, 0, 0, 1, 2, 3, 4, 4, 5, 5, 4, 3, 3, 4, 4, 5, 6, 6, 7, 7, 6, 5, 5, 6, 6, 5, 4, 3, 2, 2, 3, 3, 2, 1, 1, 2, 2, 3, 4, 4, 5, 5, 4, 3

Offset

0,11

Comments

We consider a hexagonal lattice with X-axis and Y-axis as follows:

Y

/

/

0 ---- X

We define the family {H_n, n > 0} as follows:

- T_1 contains the origin (0, 0) and (1, 0), in that order:

+-->--+

O

- for any n > 0, H_{n+1} is built from 4 copies of H_n connected with 2^(n+1) unit segments as follows:

+->-2->-+

\ /

^ v

\ /

+->-1->-+->-4->-+

O / \

v ^

/ \

+->-3->-+

- H is the limit of H_n as n tends to infinity,

- H visits once every unit segment (u, v) where u and v are lattice points and at least one of u or v belongs to the region { (x, y) | x > 0 or x + y > 0 }.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..12160

Rémy Sigrist, PARI program for A339456

Index entries for sequences related to coordinates of 2D curves

Prog

(PARI) See Links section.

Crossrefs

Cf. A339455.

Sequence in context: A191860 A109973 A340488 * A220517 A369053 A340328

Adjacent sequences: A339453 A339454 A339455 * A339457 A339458 A339459

Keyword

sign,look

Author

Rémy Sigrist, Dec 06 2020

Status

approved