A339455 -id:A339455 - cp's OEIS frontend

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

Rémy Sigrist, Dec 06 2020

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 }.

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

Cf. A339455.

PARI
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cp's OEIS Frontend

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.

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