cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A349319 a(n) is the X-coordinate of the n-th point of the hexdragon curve; sequence A349320 gives Y-coordinates.

Original entry on oeis.org

0, 1, 1, 0, 0, 1, 1, 0, -1, -1, -2, -3, -3, -2, -2, -3, -3, -2, -2, -3, -4, -4, -5, -6, -7, -7, -6, -5, -4, -4, -5, -6, -7, -7, -8, -9, -9, -8, -8, -9, -9, -8, -8, -9, -10, -10, -11, -12, -12, -11, -11, -12, -12, -11, -11, -12, -13, -13, -14, -15, -16, -16
Offset: 0

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Author

Rémy Sigrist, Nov 14 2021

Keywords

Comments

Coordinates are given on a hexagonal lattice with X-axis and Y-axis as follows (the Y-axis corresponds to the sixth primitive root of unity):
Y
/
/
0 ---- X
The hexdragon curve can be represented using an L-system obtained from that of the terdragon curve by replacing each "move forward and turn +-120 degrees" step by two "move forward and turn +- 60 degrees" steps.

Examples

			The hexdragon curve starts as follows:
              16-17
              /
            15
              \
              14
              /
         12-13
         /
       11      8--7
         \    /    \
         10--9      6
                   /
               4--5
              /
             3
              \
               2
              /
          0--1
- so a(0) = a(3) = a(4) = a(7) = 0,
     a(1) = a(2) = a(5) = a(6) = 1,
     a(8) = a(9) = -1,
     a(10) = a(13) = a(14) = a(17) = -2,
     a(11) = a(12) = a(15) = a(16) = -3.
		

Crossrefs

See A349040 for a similar sequence.
Cf. A349320.

Programs

  • PARI
    See Links section.
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