A005615 Number of non-degenerate fanout-free Boolean functions of n variables using And, Or, Not and Majority gates.

2, 2, 8, 72, 1152, 26304, 773376, 27792384, 1180606464, 57878949888, 3216287711232, 199772566437888, 13715535726379008, 1031385107381354496, 84305991898648018944, 7442748678347943837696, 705753951277588515127296, 71539473538360558749745152

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

A circuit is fanout-free if each gate's output is the input to (at most) one gate. - Charles R Greathouse IV, Jul 21 2016

A majority gate has 3 inputs and the output is the same as the majority of the inputs. - Andrew Howroyd, Apr 04 2025

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
• E. A. Bender and J. T. Butler, Asymptotic approximations for the number of fanout-free functions, IEEE Trans. Computers, 27 (1978), 1180-1183. (Annotated scanned copy)
• J. T. Butler, Letter to N. J. A. Sloane, Dec. 1978.
• 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. A005742, A005743.

Programs

PARI

seq(n)=Vec(serlaplace(2 + serreverse(log(x+1+O(x*x^n)) - x/2 - x^3/12))) \\ Andrew Howroyd, Apr 04 2025

Formula

E.g.f.: 2 + Series_Reversion(log(1 + x) - x/2 - x^3/12). - Andrew Howroyd, Apr 04 2025

Extensions

a(0), a(8)-a(17) from Sean A. Irvine, Jul 21 2016