A334486 a(n) is the Y-coordinate of the n-th point of Gosper's flowsnake curve; sequence A334485 gives X-coordinates.

0, 0, 1, 1, 2, 2, 2, 1, 1, 2, 3, 3, 2, 3, 4, 5, 5, 5, 4, 4, 3, 3, 4, 4, 3, 2, 3, 4, 5, 5, 6, 6, 7, 7, 7, 6, 6, 7, 7, 8, 8, 8, 7, 6, 5, 4, 5, 6, 6, 5, 5, 6, 6, 7, 7, 7, 6, 6, 7, 8, 8, 7, 8, 9, 9, 10, 11, 11, 10, 11, 12, 13, 13, 13, 12, 12, 11, 11, 10, 9, 10, 10

Offset: 0

Author

Rémy Sigrist, May 03 2020

Keywords

• nonn

Comments

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

Y

/

/

0 ---- X

Examples

			The Gosper curve starts (on a hexagonal lattice) as follows:
     .   .   .   .   .   +---+---+   .   .   .   .
                          \       \
       .   .   +---+---+   +---+   +   .   .   .   .
                \       \     /   /
     .   .   .   +---+   +---+   +   +---+   .   .
                    /             \   \   \
       .   .   +---+   +---+---+   +   +   +   .   .
              /         \       \   \ /    49
     .   .   +   +---+   +---+   +   +   .   .   .
              \   \   \     /   /
       .   .   +   +   +---+   +   +---+   .   .   .
                \ /             \ /   /10
     .   .   .   +   +---+---+   +   +   .   .   .
                 25   \       \     /9
       .   .   .   .   +---+   +---+   .   .   .   .
                          /    7   8
     .   .   .   .   +---+   .   .   .   .   .   .
                     0   1
- hence a(2) = a(3) = a(7) = a(8) = 1.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..2401
• Rémy Sigrist, PARI program for A334486
• Wikipedia, Gosper curve
• Index entries for sequences related to coordinates of 2D curves

Crossrefs

Cf. A334485 (X coordinate), A229214 (direction +-1,2,3), A261180 (direction 0..5).

Programs

PARI

See Links section.