A309111 Number of possible permutations of a Corner-turning Octahedron of size n, disregarding the trivial rotation of the tips.

1, 1, 2009078326886400, 25130033447370922318407480728239472640000000, 5759627596191312699511553760965199283079808523515804251057792885981184000000000000000

Offset

1,3

Comments

a(6) has 140 digits and a(7) has 203 digits.

The Corner-turning 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 Face-turning Octahedron are perpendicular to the faces. As a result, the only rotation of the Corner-turning Octahedron of size 2 is the trivial rotation of the tips (it is not the same of the Skewb Diamond, the Face-turning 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*n-6) * a(n-3) for n >= 6.

Let A = 258369126400, then for n >= 3: a(n) = A * 6^(-8*n^2/3+16*n-19) * (24!)^(n^2/3-n) if 3 divides n, otherwise a(n) = A * 560 * 6^(-8*n^2+16*n-43/3) * (24!)^(n^2/3-n-1/3).

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*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

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: A067495 A335044 A216910 * A047698 A246252 A058445

Adjacent sequences: A309108 A309109 A309110 * A309112 A309113 A309114

Keyword

nonn

Author

Jianing Song, Jul 13 2019

Status

approved