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.
%I A245079 #58 May 02 2025 01:26:00
%S A245079 2,4,14,104,2170,230540,499596550,309075799150640,
%T A245079 14369391928071394429416818,
%U A245079 146629927766168786368451678290041110762316052
%N A245079 Number of bipolar Boolean functions, that is, Boolean functions that are monotone or antimonotone in each argument.
%C A245079 A Boolean function is bipolar if and only if for each argument index i, the function is one of: (1) monotone in argument i, (2) antimonotone in argument i, (3) both monotone and antimonotone in argument i.
%C A245079 These functions are variously called "unate functions" or "locally monotone functions". - _Aniruddha Biswas_, May 11 2024
%D A245079 Richard Dedekind, Über Zerlegungen von Zahlen durch ihre grössten gemeinsamen Theiler, in Fest-Schrift der Herzoglichen Technischen Hochschule Carolo-Wilhelmina, pages 1-40. Vieweg+Teubner Verlag (1897).
%H A245079 Ringo Baumann and Hannes Strass, <a href="https://doi.org/10.1093/logcom/exx025">On the Number of Bipolar Boolean Functions</a>, Journal of Logic and Computation, exx025. Also available as a <a href="https://iccl.inf.tu-dresden.de/w/images/a/ab/HS1112620917_2017_JLC-16-40.pdf">Preprint</a>.
%H A245079 Aniruddha Biswas and Palash Sarkar, <a href="https://arxiv.org/abs/2304.14069">Counting unate and balanced monotone Boolean functions,</a> arXiv:2304.14069 [math.CO], 2023.
%H A245079 Aniruddha Biswas and Palash Sarkar, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL28/Biswas/biswas6.html">Counting Unate and Monotone Boolean Functions Under Restrictions of Balancedness and Non-Degeneracy</a>, J. Int. Seq. (2025) Vol. 28, Art. No. 25.3.4. See pp. 2, 4, 12.
%H A245079 Gerhard Brewka and Stefan Woltran, <a href="http://aaai.org/ocs/index.php/KR/KR2010/paper/view/1294">Abstract dialectical frameworks</a>, Proceedings of the Twelfth International Conference on the Principles of Knowledge Representation and Reasoning. Pages 102--111. IJCAI/AAAI 2010.
%F A245079 a(n) = Sum_{i=1..n}(2^i * C(n,i) * A006126(i)) + 2.
%e A245079 There are 2 bipolar Boolean functions in 0 arguments, the constants true and false.
%e A245079 All 4 Boolean functions in one argument are bipolar.
%e A245079 For 2 arguments, only equivalence and exclusive-or are not bipolar, 16-2=14.
%Y A245079 Cf. A006126.
%K A245079 nonn,hard,more
%O A245079 0,1
%A A245079 _Hannes Strass_, Jul 11 2014
%E A245079 a(7)-a(8) corrected by and a(9) from _Aniruddha Biswas_, May 11 2024