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A334483
a(n) is the X-coordinate of the n-th point of the Sierpinski arrowhead curve; sequence A334484 gives Y-coordinates.
2
0, 1, 1, 0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 7, 7, 6, 5, 4, 4, 3, 2, 2, 1, 0, 0, 1, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 1, 0, 0, 1, 2, 2, 3, 4, 5, 5, 4, 4, 5, 6, 6, 7, 8, 8, 9, 10, 11, 11, 10, 9, 8, 8, 9, 9, 8, 8, 9, 10, 10, 11, 12, 13, 13, 12, 12, 13, 14, 14, 15
OFFSET
0,7
COMMENTS
Coordinates are given on a hexagonal lattice with X-axis and Y-axis as follows:
Y
/
/
0 ---- X
The Sierpinski arrowhead curve can be represented using an L-system.
FORMULA
A262174(1 + a(n) + A334484(n), 1 + A334484(n)) = 1 + n for any n >= 0.
EXAMPLE
The Sierpinski arrowhead curve starts (on a hexagonal lattice) as follows:
+
27\
\
+
/26
/
+----+
/24 25
/
+ +----+
23\ /20 19\
\ / \
+----+ +
22 21 /18
/
+----+ +
/4 5\ 17\
/ \ \
+ + +----+
3\ /6 16 15\
\ / \
+ + +----+ +
/2 7\ /10 11\ /14
/ \ / \ /
+----+ +----+ +----+
0 1 8 9 12 13
- hence a(6) = a(7) = a(20) = a(21) = 2.
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Rémy Sigrist, May 03 2020
STATUS
approved