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

%I A005615 M1899 #45 Apr 04 2025 01:19:33
%S A005615 2,2,8,72,1152,26304,773376,27792384,1180606464,57878949888,
%T A005615 3216287711232,199772566437888,13715535726379008,1031385107381354496,
%U A005615 84305991898648018944,7442748678347943837696,705753951277588515127296,71539473538360558749745152
%N A005615 Number of non-degenerate fanout-free Boolean functions of n variables using And, Or, Not and Majority gates.
%C A005615 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
%C A005615 A majority gate has 3 inputs and the output is the same as the majority of the inputs. - _Andrew Howroyd_, Apr 04 2025
%D A005615 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005615 Andrew Howroyd, <a href="/A005615/b005615.txt">Table of n, a(n) for n = 0..200</a>
%H A005615 E. A. Bender and J. T. Butler, <a href="/A005612/a005612.pdf">Asymptotic approximations for the number of fanout-free functions</a>, IEEE Trans. Computers, 27 (1978), 1180-1183. (Annotated scanned copy)
%H A005615 J. T. Butler, <a href="/A005607/a005607_1.pdf">Letter to N. J. A. Sloane, Dec. 1978</a>.
%H A005615 K. L. Kodandapani and S. C. Seth, <a href="http://doi.ieeecomputersociety.org/10.1109/TC.1978.1675103">On combinational networks with restricted fan-out</a>, IEEE Trans. Computers, 27 (1978), 309-318. (<a href="/A005736/a005736.pdf">Annotated scanned copy</a>)
%H A005615 <a href="/index/Bo#Boolean">Index entries for sequences related to Boolean functions</a>
%F A005615 E.g.f.: 2 + Series_Reversion(log(1 + x) - x/2 - x^3/12). - _Andrew Howroyd_, Apr 04 2025
%o A005615 (PARI) seq(n)=Vec(serlaplace(2 + serreverse(log(x+1+O(x*x^n)) - x/2 - x^3/12))) \\ _Andrew Howroyd_, Apr 04 2025
%Y A005615 Cf. A005742, A005743.
%K A005615 nonn
%O A005615 0,1
%A A005615 _N. J. A. Sloane_
%E A005615 a(0), a(8)-a(17) from _Sean A. Irvine_, Jul 21 2016