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

%I A381367 #28 Mar 03 2025 13:33:13
%S A381367 43252003274489856000,
%T A381367 1756772880709135843168526079081025059614484630149557651477156021733236798970168550600274887650082354207129600000000000000
%N A381367 Number of possible configurations of an n dimensional Rubik's hypercube.
%C A381367 a(4) was calculated by Kamack and Keane (1982) and Velleman (1992). - _Amiram Eldar_, Mar 03 2025
%H A381367 Amiram Eldar, <a href="/A381367/b381367.txt">Table of n, a(n) for n = 3..5</a>
%H A381367 Harry J. Kamack and Tom R. Keane, <a href="https://citeseerx.ist.psu.edu/document?repid=rep1&amp;type=pdf&amp;doi=71cda647f3274881b2c78fb023a8895657b29968">The Rubik tesseract</a>, unpublished manuscript, 1982; <a href="https://udel.edu/~tomkeane/RubikTesseract.pdf">alternative link</a>.
%H A381367 Giovanni Luca Marchetti, <a href="https://arxiv.org/abs/2502.13518">Rubik's Abstract Polytopes</a>, arXiv:2502.13518 [math.CO], 2025.
%H A381367 Dan Velleman, <a href="https://www.jstor.org/stable/2691357">Rubik's Tesseract</a>, Mathematics Magazine, Vol. 65, No. 1 (1992), pp. 27-36.
%H A381367 Googology Wiki, <a href="https://googology.fandom.com/wiki/Twisty_puzzle-related_numbers">Twisty puzzle-related numbers</a>.
%F A381367 See formula (26) on p. 16 of Marchetti.
%t A381367 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 *)
%o A381367 (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))));
%Y A381367 Cf. A075152 (for a(3)), A381366.
%K A381367 nonn
%O A381367 3,1
%A A381367 _Michel Marcus_, Feb 21 2025