OFFSET
0,7
COMMENTS
We consider a hexagonal lattice with X-axis and Y-axis as follows:
Y
/
/
0 ---- X
We define the family {H_n, n > 0} as follows:
- T_1 contains the origin (0, 0) and (1, 0), in that order:
+-->--+
O
- for any n > 0, H_{n+1} is built from 4 copies of H_n connected with 2^(n+1) unit segments as follows:
+->-2->-+
\ /
^ v
\ /
+->-1->-+->-4->-+
O / \
v ^
/ \
+->-3->-+
- H is the limit of H_n as n tends to infinity,
- H visits once every unit segment (u, v) where u and v are lattice points and at least one of u or v belongs to the region { (x, y) | x > 0 or x + y > 0 },
- the n-th segment of curve H has length 2^A235127(n).
LINKS
Rémy Sigrist, Table of n, a(n) for n = 0..3008
Rémy Sigrist, Illustration of H_3
Rémy Sigrist, PARI program for A339455
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Dec 06 2020
STATUS
approved