A005736 Number of degenerate fanout-free Boolean functions of n variables using And, Or and Not gates.

0, 2, 6, 32, 314, 4892, 104518, 2814520, 91069042, 3434371508, 147755228670, 7137203824016, 382309275191786, 22484502178536140, 1440083130444110134, 99761235465965943400, 7431676025141300550370, 592372327653418546022756

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

References

• J. P. Hayes, Enumeration of fanout-free Boolean functions, J. ACM, 23 (1976), 700-709.
• 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. A005640, A005737, A224766.

Formula

a(n) = Sum_{k=0..n-1} binomial(n, k) * s(k) where s(0)=2 and s(n) = A005640(n + 1) otherwise. - Sean A. Irvine, Jul 21 2016

a(n) = A005737(n) - A224766(n). - Andrew Howroyd, Mar 29 2025

Extensions

More terms from Sean A. Irvine, Jul 21 2016

Name clarified by Andrew Howroyd, Apr 03 2025