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%I #25 Jul 28 2024 00:44:45
%S 2,4,10,34,200,3466,829744
%N Number of inequivalent unate functions of n or fewer variables.
%C A Boolean function is unate in a variable if it is either nondecreasing or nonincreasing with respect to that variable. Therefore in the circuit representation of unate functions, each variable appears either in its original form or in complemented form. Thus 𝑥⊕𝑦=(𝑥∧¬𝑦)∨(¬𝑥∧𝑦) is not a unate function.
%C Moreover, two Boolean functions are said to be equivalent if they are equivalent under the permutation of variables. For example, 𝑓(𝑥,𝑦)=𝑥 is equivalent to 𝑓(𝑥,𝑦)=𝑦 under the permutation of input variables.
%H 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 <a href="/index/Bo#Boolean">Index entries for sequences related to Boolean functions</a>
%e The list of all 2-variable inequivalent unate functions f(x,y) is 0,1,x,¬x,x∧y,¬x∧y,¬x∧¬y,x∨y,¬x∨y,¬x∨¬y. So a(2)=10.
%Y Cf. A000372, A003182, A245079.
%K nonn,hard,more
%O 0,1
%A _Aniruddha Biswas_, May 03 2024