A309110 - OEIS

%I #15 Aug 24 2019 14:25:08

%S 1,81,75582720,217225462874112000,19228688422470957567836160000000,

%T 52425105093745505455227317179687895040000000000000,

%U 20582183665033346731252760185588627707250626464317440000000000000000000

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

%C 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).

%H Amiram Eldar, <a href="/A309110/b309110.txt">Table of n, a(n) for n = 1..23</a>

%H Michael Gottlieb, <a href="https://michael-gottlieb.blogspot.com/2008/05/number-of-positions-of-generalized.html">Notes on Twisty Puzzles</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Pyraminx">Pyraminx</a>

%F a(n) = 272097792 * 369600^(2*n-6) * a(n-3) for n >= 6.

%F a(n) = 81 * A309109(n) for n >= 2.

%o (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)))))

%Y 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).

%K nonn

%O 1,2

%A _Jianing Song_, Jul 13 2019