cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A005617 Number of non-degenerate fanout-free Boolean functions of n variables using And, Or, Xor, Not, and Majority gates.

Original entry on oeis.org

2, 2, 10, 122, 2554, 75386, 2865370, 133191386, 7319102842, 464161640378, 33365010466330, 2680736773291418, 238072159069838266, 23157446685020355194, 2448496007747625525850, 279603850797891071481434, 34294941015273001096282618
Offset: 0

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Author

Keywords

References

  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Crossrefs

Programs

  • 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

A005738 Number of degenerate fanout-free Boolean functions of n variables using And, Or, Xor, and Not gates.

Original entry on oeis.org

0, 2, 6, 38, 526, 12022, 376430, 14821942, 700501294, 38564486966, 2421312598894, 170655141398326, 13336218401711534, 1144162670908970806, 106893046255965640174, 10800877688088297157430, 1173551859231328950561838, 136431643427143746045393718
Offset: 0

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Author

Keywords

Comments

Number of degenerate disjunctively-realizable functions of n variables.

References

  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Crossrefs

Formula

a(n) = Sum_{k=0..n-1} binomial(n,k) * A005616(k). [From Kodandapani and Seth] - Sean A. Irvine, Jul 21 2016
a(n) = A005739(n) - A005616(n). - Andrew Howroyd, Apr 03 2025

Extensions

More terms from Sean A. Irvine, Jul 21 2016
a(0) prepended and definition clarified by Andrew Howroyd, Apr 03 2025

A005739 Number of disjunctively-realizable functions of n variables.

Original entry on oeis.org

2, 4, 16, 152, 2680, 68968, 2311640, 95193064, 4645069336, 261938616104, 16756882325464, 1198897678224232, 94851206834082200, 8221740727881348520, 774839374768829174104, 78880995816162599086568, 8626562553228821851608856
Offset: 0

Views

Author

Keywords

Comments

Number of fanout-free Boolean functions of n variables using And, Or, Xor, and Not gates. - Andrew Howroyd, Apr 03 2025

References

  • K. L. Kodandapani and S. C. Seth, On combinational networks with restricted fan-out, IEEE Trans. Computers, C-27 (1978), 309-318.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Crossrefs

Formula

a(n) = A005616(n) + A005738(n) [From Kodandapani and Seth]. - Sean A. Irvine, Jul 21 2016
Binomial transform of A005616. - Andrew Howroyd, Apr 03 2025

Extensions

More terms from Sean A. Irvine, Jul 21 2016
a(0)=2 prepended by Andrew Howroyd, Apr 03 2025
Showing 1-3 of 3 results.