A005617 Number of non-degenerate fanout-free Boolean functions of n variables using And, Or, Xor, Not, and Majority gates.
2, 2, 10, 122, 2554, 75386, 2865370, 133191386, 7319102842, 464161640378, 33365010466330, 2680736773291418, 238072159069838266, 23157446685020355194, 2448496007747625525850, 279603850797891071481434, 34294941015273001096282618
Offset: 0
Keywords
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
Programs
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PARI
seq(n)=Vec(2*serlaplace(1 + serreverse(log(1 + 3*x + 2*x^2 + O(x*x^n)) - 2*x - 2*x^3/3))) \\ Andrew Howroyd, Apr 04 2025
Formula
E.g.f.: 2 + 2*Series_Reversion(log(1 + 3*x + 2*x^2) - 2*x - 2*x^3/3). - Andrew Howroyd, Apr 04 2025
Extensions
a(0) prepended and more terms from Sean A. Irvine, Jul 21 2016