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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

Amiram Eldar, Table of n, a(n) for n = 1..14

Michael Gottlieb's blogger, Notes on Twisty Puzzles

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).

Sequence in context: A017304 A017424 A017556 * A044887 A217196 A321809

Adjacent sequences:  A309109 A309110 A309111 * A309113 A309114 A309115

KEYWORD

nonn

AUTHOR

Jianing Song, Jul 13 2019

STATUS

approved

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Last modified September 25 22:38 EDT 2020. Contains 337346 sequences. (Running on oeis4.)