OFFSET
1,2
COMMENTS
a(6) has 143 digits and a(7) has 207 digits.
Comment rewritten by Jianing Song, Feb 21 2025: (Start)
The Corner-Turning Octahedron is a regular octahedron puzzle in the style of Rubik's Cube. The octahedron is cut by 6 groups of n-1 equally-spaced planes not passing through the center, where the planes in each group are perpendicular to one of the 3 lines connecting a pair of opposite vertices of the octahedron. In comparison, the regular octahedron is cut by 4 groups of n-1 equally-spaced planes for the Face-Turning Octahedron of size n, where the planes in each group are parallel to one of the 4 pairs of opposite faces of the octahedron. As a result, the Corner-Turning Octahedron of size 2 is not the same of the Skewb Diamond, the Face-Turning Octahedron of size 2: its only rotations are the trivial rotations of the tips.
For n >= 3, see the Michael Gottlieb link below for an explanation of the term a(n). (End)
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..14
Michael Gottlieb's blogger, Notes on Twisty Puzzles
FORMULA
a(n) = 6^(-16*n+72) * (24!)^(2*n-6) * a(n-3) for n >= 6.
a(n) = 4096 * A309111(n) for n >= 2.
EXAMPLE
See the Michael Gottlieb link above.
PROG
(PARI) a(n) = if(n==1, 1, 4096 * (if(n==2, 1, my(A = 258369126400); if(!(n%3), A * 6^(-8*n^2/3+16*n-19) * (24!)^(n^2/3-n), A * 560 * 6^(-8*n^2/3+16*n-43/3) * (24!)^(n^2/3-n-1/3)))))
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Jianing Song, Jul 13 2019
STATUS
approved