A005738 Number of degenerate fanout-free Boolean functions of n variables using And, Or, Xor, and Not gates.

0, 2, 6, 38, 526, 12022, 376430, 14821942, 700501294, 38564486966, 2421312598894, 170655141398326, 13336218401711534, 1144162670908970806, 106893046255965640174, 10800877688088297157430, 1173551859231328950561838, 136431643427143746045393718

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Number of degenerate disjunctively-realizable functions of n variables.

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200
• K. L. Kodandapani and S. C. Seth, On combinational networks with restricted fan-out, IEEE Trans. Computers, 27 (1978), 309-318. (Annotated scanned copy)
• Index entries for sequences related to Boolean functions

Crossrefs

Cf. A005616, A005739.

Formula

a(n) = Sum_{k=0..n-1} binomial(n,k) * A005616(k). [From Kodandapani and Seth] - Sean A. Irvine, Jul 21 2016

a(n) = A005739(n) - A005616(n). - Andrew Howroyd, Apr 03 2025

Extensions

More terms from Sean A. Irvine, Jul 21 2016

a(0) prepended and definition clarified by Andrew Howroyd, Apr 03 2025