|
| |
|
|
A309112
|
|
Number of possible permutations of a Corner-turning Octahedron of size n, including the trivialrotation of the tips.
|
|
6
|
|
|
|
1, 4096, 8229184826926694400, 102932617000431297816197041062868879933440000000, 23591434633999616817199324204913456263494895712320734212332719660978929664000000000000000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
a(6) has 143 digits and a(7) has 207 digits.
The Corner-turning Octahedron is a regular octahedron puzzle in the style of Rubik's Cube. The rotational axes of the pieces are parallel to the lines connecting a pair of opposite vertices. In comparison, the rotational axes of the Face-turning Octahedron are perpendicular to the faces. As a result, the only rotation of the Corner-turning Octahedron of size 2 is the trivial rotation of the tips (it is not the same of the Skewb Diamond, the Face-turning Octahedron of size 2). For n >= 3, see the Michael Gottlieb link below for an explanation of the term a(n).
|
|
|
LINKS
|
|
|
|
FORMULA
|
a(n) = 6^(-16*n+72) * (24!)^(2*n-6) * a(n-3) for n >= 6.
a(n) = 4096 * A309111(n) for n >= 2.
|
|
|
EXAMPLE
|
See the Michael Gottlieb link above.
|
|
|
PROG
|
(PARI) a(n) = if(n==1, 1, 4096 * (if(n==2, 1, my(A = 258369126400); if(!(n%3), A * 6^(-8*n^2/3+16*n-19) * (24!)^(n^2/3-n), A * 560 * 6^(-8*n^2/3+16*n-43/3) * (24!)^(n^2/3-n-1/3)))))
|
|
|
CROSSREFS
|
Number of possible permutations of: tetrahedron puzzle (without tips: A309109, with tips: A309110); cube puzzle (A075152); octahedron puzzle (without tips: A309111, with tips: this sequence); dodecahedron (A309113).
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
