

A309111


Number of possible permutations of a Cornerturning Octahedron of size n, disregarding the trivial rotation of the tips.


5




OFFSET

1,3


COMMENTS

a(6) has 140 digits and a(7) has 203 digits.
The Cornerturning Octahedron is a regular octahedron puzzle in the style of Rubik's Cube. The rotational axes of the pieces are parallel to the lines connecting a pair of opposite vertices. In comparison, the rotational axes of the Faceturning Octahedron are perpendicular to the faces. As a result, the only rotation of the Cornerturning Octahedron of size 2 is the trivial rotation of the tips (it is not the same of the Skewb Diamond, the Faceturning Octahedron of size 2). For n >= 3, see the Michael Gottlieb link below for an explanation of the term a(n).


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*n6) * a(n3) for n >= 6.
Let A = 258369126400, then for n >= 3: a(n) = A * 6^(8*n^2/3+16*n19) * (24!)^(n^2/3n) if 3 divides n, otherwise a(n) = A * 560 * 6^(8*n^2+16*n43/3) * (24!)^(n^2/3n1/3).


EXAMPLE

See the Michael Gottlieb link above.


PROG

(PARI) a(n) = if(n<=2, 1, my(A = 258369126400); if(!(n%3), A * 6^(8*n^2/3+16*n19) * (24!)^(n^2/3n), A * 560 * 6^(8*n^2/3+16*n43/3) * (24!)^(n^2/3n1/3)))


CROSSREFS

Number of possible permutations of: tetrahedron puzzle (without tips: A309109, with tips: A309110); cube puzzle (A075152); octahedron puzzle (without tips: this sequence, with tips: A309112); dodecahedron (A309113).
Sequence in context: A204419 A067495 A216910 * A047698 A246252 A058445
Adjacent sequences: A309108 A309109 A309110 * A309112 A309113 A309114


KEYWORD

nonn


AUTHOR

Jianing Song, Jul 13 2019


STATUS

approved



