A005616 Number of non-degenerate disjunctively-realizable functions of n variables.
2, 2, 10, 114, 2154, 56946, 1935210, 80371122, 3944568042, 223374129138, 14335569726570, 1028242536825906, 81514988432370666, 7077578056972377714, 667946328512863533930, 68080118128074301929138, 7453010693997492901047018
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, Jun. 1975 and Dec. 1978.
- J. T. Butler, On the number of functions realized by cascades and disjunctive networks, IEEE Trans. Computers, C-24 (1975), 681-690. (Annotated scanned copy)
- K. L. Kodandapani and S. C. Seth, On combinational networks with restricted fan-out, IEEE Trans. Computers, 27 (1978), 309-318. (Annotated scanned copy)
Programs
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PARI
seq(n)=my(p=2*exp(x + O(x*x^n)), g=serreverse(x + log(p-1) - p + 2)); Vec(serlaplace(2*exp(g))) \\ Andrew Howroyd, Apr 03 2025
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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))) \\ Andrew Howroyd, Apr 03 2025
Formula
From Andrew Howroyd, Apr 03 2025: (Start)
E.g.f.: 2*(p + q + 1) where p,q satisfy q = exp(p) - p - 1, p = exp(2*q + p + x) - (2*q + p + 1).
E.g.f.: 2*exp( Series_Reversion(x + log(2*exp(x)-1) - 2*(exp(x) - 1)) ).
E.g.f.: 2 + 2*Series_Reversion(log(1 + 3*x + 2*x^2) - 2*x). (End)
Extensions
a(0), a(14)-a(16) from Sean A. Irvine, Jul 21 2016
Comments