A309109 Number of possible permutations of a Pyraminx of size n, disregarding the trivial rotation of the tips.

1, 1, 933120, 2681795837952000, 237391215092234044047360000000, 647223519675870437718855767650467840000000000000, 254101032901646255941392101056649724780871931658240000000000000000000

Offset

1,3

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) = 5 * 2^(2*n^2-3*n-1) * 3^(n^2/3+3*n-6) * 1925^(n^2/3-n) if 3 divides n, otherwise a(n) = 5 * 2^(2*n^2-3*n-1) * 3^(n^2/3+3*n-16/3) * 1925^(n^2/3-n-1/3).

Prog

(PARI) a(n) = 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: this sequence, with tips: A309110); cube puzzle (A075152); octahedron puzzle (without tips: A309111, with tips: A309112); dodecahedron (A309113).

Sequence in context: A029818 A130672 A158125 * A075008 A244564 A104929

Adjacent sequences: A309106 A309107 A309108 * A309110 A309111 A309112

Keyword

nonn

Author

Jianing Song, Jul 13 2019

Status

approved