A381366 Number of possible configurations of an n dimensional Rubik's simplex.

3732480, 253603223500400479331942400000, 66038535945066815418194228229716898861828197815802983951534337590785326501068800000000000000000

Offset: 3

Author

Michel Marcus, Feb 21 2025

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 3..7
• Giovanni Luca Marchetti, Rubik's Abstract Polytopes, arXiv:2502.13518 [math.CO], 2025.

Crossrefs

Cf. A079746 (for a(3)=3732480), A381367.

Programs

Mathematica

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

PARI

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

Formula

See formula (18) on p. 14 of Marchetti.