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A309110
Number of possible permutations of a Pyraminx of size n, including the trivial rotation of the tips.
6
1, 81, 75582720, 217225462874112000, 19228688422470957567836160000000, 52425105093745505455227317179687895040000000000000, 20582183665033346731252760185588627707250626464317440000000000000000000
OFFSET
1,2
COMMENTS
The Pyraminx is a regular tetrahedron puzzle in the style of Rubik's Cube. The rotational axes of the pieces are perpendicular to the faces. As a result, the only rotation of the Pyraminx of size 2 is the trivial rotation of the tips (it is not the same as the Pyramorphix, which is totally a different puzzle). For n >= 3, see the Michael Gottlieb link below for an explanation of the term a(n).
LINKS
Michael Gottlieb, Notes on Twisty Puzzles
Wikipedia, Pyraminx
FORMULA
a(n) = 272097792 * 369600^(2*n-6) * a(n-3) for n >= 6.
a(n) = 81 * A309109(n) for n >= 2.
PROG
(PARI) a(n) = if(n==1, 1, 81 * if(n==2, 1, 5 * (if(!(n%3), 2^(2*n^2-3*n-1) * 3^(n^2/3+3*n-6) * 1925^(n^2/3-n), 2^(2*n^2-3*n-1) * 3^(n^2/3+3*n-16/3) * 1925^(n^2/3-n-1/3)))))
CROSSREFS
Number of possible permutations of: tetrahedron puzzle (without tips: A309109, with tips: this sequence); cube puzzle (A075152); octahedron puzzle (without tips: A309111, with tips: A309112); dodecahedron (A309113).
Sequence in context: A277843 A277844 A162284 * A116268 A128838 A231484
KEYWORD
nonn
AUTHOR
Jianing Song, Jul 13 2019
STATUS
approved