A381366 Number of possible configurations of an n dimensional Rubik's simplex.
3732480, 253603223500400479331942400000, 66038535945066815418194228229716898861828197815802983951534337590785326501068800000000000000000
Offset: 3
Keywords
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.
Programs
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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.