A335381 a(n) is the Y-coordinate of the n-th point of the Kochawave curve; sequence A335380 gives X-coordinates.

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

Offset: 0

Author

Rémy Sigrist, Jun 04 2020

Keywords

• nonn

Comments

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

Y

/

/

0 ---- X

Examples

			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.
		

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

Crossrefs

Cf. A335380.

Programs

PARI

See Links section.

Formula

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