A381367 Number of possible configurations of an n dimensional Rubik's hypercube.

43252003274489856000, 1756772880709135843168526079081025059614484630149557651477156021733236798970168550600274887650082354207129600000000000000

Offset: 3

Author

Michel Marcus, Feb 21 2025

Keywords

• nonn

Comments

a(4) was calculated by Kamack and Keane (1982) and Velleman (1992). - Amiram Eldar, Mar 03 2025

Links

• Amiram Eldar, Table of n, a(n) for n = 3..5
• Harry J. Kamack and Tom R. Keane, The Rubik tesseract, unpublished manuscript, 1982; alternative link.
• Giovanni Luca Marchetti, Rubik's Abstract Polytopes, arXiv:2502.13518 [math.CO], 2025.
• Dan Velleman, Rubik's Tesseract, Mathematics Magazine, Vol. 65, No. 1 (1992), pp. 27-36.
• Googology Wiki, Twisty puzzle-related numbers.

Crossrefs

Cf. A075152 (for a(3)), A381366.

Programs

Mathematica

a[n_] := (1/(If[n >= 5, 1, 3]*2^(2^n + 2*(n-2)))) * Product[(n-i)!^(2^(n-i)*Binomial[n, i])*(2^(n-i) * Binomial[n, i])!, {i, 0, n-2}]; Array[a, 2, 3] (* Amiram Eldar, Feb 21 2025 *)

PARI

a(n) = my(c=1); if (n<5, c=3); prod(i=0, n-2, ((n-i)!)^((2^(n-i)*binomial(n,i)))*((2^(n-i)*binomial(n,i))!))/(c*(2^(2^n+2*(n-2))));

Formula

See formula (26) on p. 16 of Marchetti.