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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.
2
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
0,11
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.
EXAMPLE
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.
PROG
(PARI) See Links section.
CROSSREFS
See A349040 for a similar sequence.
Cf. A349320.
Sequence in context: A269043 A309952 A059252 * A251619 A030620 A348241
KEYWORD
sign
AUTHOR
Rémy Sigrist, Nov 14 2021
STATUS
approved