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
KEYWORD
nonn
AUTHOR
Jianing Song, Jul 13 2019
STATUS
approved