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A343310
a(n) is the number of bilaterally symmetrical self-avoiding paths connecting consecutive corners of an n X n triangular grid.
2
1, 2, 4, 12, 50, 264, 2054, 22324, 377704, 9455172, 385118374, 23504746636, 2346325946460, 348814672315896, 84278783653480026, 30255270733134656280, 17646594353716082850430, 15321207204408662854455924, 21654163559101840305705453010, 45620955950222177660249163228084
OFFSET
1,2
COMMENTS
We use unit moves parallel to the triangle edges.
LINKS
FORMULA
a(n) <= A343307(n).
EXAMPLE
For n = 3:
- we have the following bilaterally symmetrical paths:
. . . . o
. / \
. . . o o o---o o o
. / \ / \ / \ / \
. o---o---o o o o o . o o . o
- so a(3) = 4.
PROG
(PARI) See Links section.
CROSSREFS
Cf. A343307.
Sequence in context: A030864 A030812 A030974 * A030843 A030887 A030924
KEYWORD
nonn,walk
AUTHOR
Rémy Sigrist, Apr 11 2021
EXTENSIONS
a(12)-a(13) from Martin Ehrenstein, May 02 2021
Terms a(14) and beyond from Andrew Howroyd, Feb 05 2022
STATUS
approved