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A362207
a(n) is the number of unordered triples of shortest nonintersecting grid paths joining two opposite corners of an n X n X n grid.
1
2, 1440, 5039744, 30456915312, 244247250106272, 2330237215901633376, 25005390829898900970720, 292102859220245236374450192, 3638369778575244135648725730848, 47651985114895805442163075548018912, 649794504408024777960179124905242154688
OFFSET
1,1
COMMENTS
An n X n X n grid is a cube with (n+1)^3 grid points. Each of the three paths has 3*n steps and they intersect only at the start and at the end. Initially, each path will start by moving along distinct coordinate axes.
CROSSREFS
The two-dimensional version of this sequence is A000891(n-1).
Sequence in context: A294089 A157494 A227247 * A294321 A272168 A173131
KEYWORD
nonn
AUTHOR
Janaka Rodrigo, Apr 11 2023
EXTENSIONS
a(4)-a(11) from Andrew Howroyd, Apr 11 2023
STATUS
approved