A309113 Number of possible permutations of a Megaminx of size 2n+1.

1, 100669616553523347122516032313645505168688116411019768627200000000000

Offset

0,2

Comments

a(3) has 264 digits and a(4) has 574 digits.

The Megaminx is a dodecahedron-shaped puzzle similar to the Rubik's Cube. The rotational axes of the pieces are perpendicular to the faces. Here only a Megaminx of odd size is considered, see the picture below showing the relationship between the Megaminx of size 2n and 2n+1.

Links

Amiram Eldar, Table of n, a(n) for n = 0..4

Michael Gottlieb's blogger, Notes on Twisty Puzzles

Jianing Song, Relationship between the Megaminx of size 2n and 2n+1

Wikipedia, Megaminx

Formula

a(0) = 1; a(n) = 30! * 20! * 60!^(n^2-1) * 5!^(-12*n^2+12*n) * 2^(28-n) * 3^19 for n > 0.

Example

See the Michael Gottlieb link above.

Prog

(PARI) a(n) = if(n, 30! * 20! * 60!^(n^2-1) * 5!^(-12*n^2+12*n) * 2^(28-n) * 3^19, 1)

Crossrefs

Number of possible permutations of: tetrahedron puzzle (without tips: A309109, with tips: A309110); cube puzzle (A075152); octahedron puzzle (without tips: A309111, with tips: A309112); dodecahedron (this sequence).

Sequence in context: A095526 A246291 A095528 * A095530 A095532 A095534

Adjacent sequences: A309110 A309111 A309112 * A309114 A309115 A309116

Keyword

nonn,bref

Author

Jianing Song, Jul 13 2019

Status

approved