A000824 Number of switching networks (see Harrison reference for precise definition). (Formerly M4917 N2110)

13, 237, 356026, 2932175712336, 412646680050205587085305856, 16346619102569481158480824333166611354489546429742186496

Offset

1,1

Comments

Number of equivalence classes with complementation of n variables on the domain and symmetric group of 3 variables operating on the range. - Sean A. Irvine, Jul 11 2011

References

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, On the number of classes of switching networks, J. Franklin Instit., 276 (1963), 313-327.

Index entries for sequences related to switching networks

Formula

Let b_n(r,s) = (2^(r*2^n) + (2^n-1)*2^(s*2^(n-1)))/2^n. Then, a(n) = (b_n(3,3) + 3*b(2,3) + 2*b(1,1))/6. - Sean A. Irvine, Jul 11 2011

Mathematica

b[n_, r_, s_] := (2^(r*2^n) + (2^n - 1)*2^(s*2^(n - 1)))/2^n; a[n_] := (b[n, 3, 3] + 3*b[n, 2, 3] + 2*b[n, 1, 1])/6; Table[a[n], {n, 6}] (* James C. McMahon, Dec 07 2023 *)

Crossrefs

Sequence in context: A218202 A134493 A051689 * A229384 A181035 A228795

Adjacent sequences: A000821 A000822 A000823 * A000825 A000826 A000827

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Jul 10 2011

Status

approved