A000723 Invertible Boolean functions of n variables.

1, 3, 840, 54486432000, 68523655451482690147713024000000, 2753622660283944533494648206058191857701074569760095316814277221684346880000000000000

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Equivalence classes of invertible maps from {0,1}^n to {0,1}^n, under action of (C_2)^n on domain and permutation of variables on range. - Sean A. Irvine, Mar 15 2011

Also the number of distinct adjacency matrices of the n-hypercube graph Q_n. - Eric W. Weisstein, Mar 31 2017

References

• M. A. Harrison, The number of classes of invertible Boolean functions, J. ACM 10 (1963), 25-28.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..8
• M. A. Harrison, The number of classes of invertible Boolean functions, J. ACM 10 (1963), 25-28. [Annotated scan of page 27 only]
• Eric Weisstein's World of Mathematics, Adjacency Matrix
• Eric Weisstein's World of Mathematics, Hypercube Graph
• Index entries for sequences related to Boolean functions

Programs

Magma

[Factorial(2^n - 1)/Factorial(n): n in [1..10]]; // Vincenzo Librandi, Mar 28 2012

Mathematica

f[n_] := (2^n - 1)!/n!; Array[f, 6] (* Robert G. Wilson v, Mar 14 2011 *)
Table[Gamma[2^n]/n!, {n, 6}] (* Eric W. Weisstein, Mar 31 2017 *)

Formula

a(n) = (2^n-1)!/n!. - Sean A. Irvine, Mar 15 2011

Extensions

More terms from Sean A. Irvine, Mar 14 2011