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A309113
Number of possible permutations of a Megaminx of size 2n+1.
6
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
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
KEYWORD
nonn,bref
AUTHOR
Jianing Song, Jul 13 2019
STATUS
approved