

A309109


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


6



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



FORMULA

a(n) = 272097792 * 369600^(2*n6) * a(n3) for n >= 6.
a(n) = 5 * 2^(2*n^23*n1) * 3^(n^2/3+3*n6) * 1925^(n^2/3n) if 3 divides n, otherwise a(n) = 5 * 2^(2*n^23*n1) * 3^(n^2/3+3*n16/3) * 1925^(n^2/3n1/3).


PROG

(PARI) a(n) = if(n<=2, 1, 5 * (if(!(n%3), 2^(2*n^23*n1) * 3^(n^2/3+3*n6) * 1925^(n^2/3n), 2^(2*n^23*n1) * 3^(n^2/3+3*n16/3) * 1925^(n^2/3n1/3))))


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).


KEYWORD

nonn


AUTHOR



STATUS

approved



