A309110 Number of possible permutations of a Pyraminx of size n, including the trivial rotation of the tips.

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

Amiram Eldar, Table of n, a(n) for n = 1..23

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

Adjacent sequences: A309107 A309108 A309109 * A309111 A309112 A309113

Keyword

nonn

Author

Jianing Song, Jul 13 2019

Status

approved