A000724 Invertible Boolean functions of n variables. (Formerly M3175 N1287)

1, 3, 196, 3406687200, 2141364232858913975435172249600, 43025354066936633335853878219659247776604712057098163541301459387254457761792000000

Offset

1,2

Comments

Equivalence classes of invertible maps from {0,1}^n to {0,1}^n, under action of (C_2)^n on domain and F_n=[S_2]^(S_n) on range. - Sean A. Irvine, Mar 16 2011

Technical report version of Harrison's paper contains incorrect value for a(4). - Sean A. Irvine, Mar 16 2011

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

Table of n, a(n) for n=1..6.

M. A. Harrison, The number of classes of invertible Boolean functions, J. ACM 10 (1963), 25-28. [Annotated scan of page 27 only]

Index entries for sequences related to Boolean functions

Formula

a(n) = ((2^n)! + (2^n-1) * (2^(n-1))! * 2^(2^(n-1)) * b(n)) / (n! * 2^(2*n)) where b(n) = n! * Sum_{k=0..floor((n-1)/2)} (2^(n-2*k)-1) / ((n - 2*k)! * k!). - Sean A. Irvine, Aug 20 2017

Mathematica

Table[((2^n)! + (2^n - 1) (2^(n - 1))! 2^(2^(n - 1)) * (n! * Sum[ (2^(n - 2 k) - 1)/((n - 2 k)!*k!), {k, 0, Floor[(n - 1)/2]}]))/(n! 2^(2 n)), {n, 6}] (* Michael De Vlieger, Aug 20 2017 *)

Crossrefs

Sequence in context: A203749 A093978 A101382 * A309749 A209120 A336250

Adjacent sequences: A000721 A000722 A000723 * A000725 A000726 A000727

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Mar 15 2011

Status

approved