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COMMENTS
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a(n) is the number of n-ary clones of the "discriminator function" t(x,y,z) defined by t(x,y,z)=x if x != y, t(x,x,z)=z.
For example, one of the 24 clones when n=3 is the function f(x,y,z)=t(t(y,z,x),x,t(x,y,z)), which has the property that f(x,x,x)=x, f(x,x,y)=y, f(x,y,x)=y, f(x,y,y)=x, f(x,y,z)=y when x,y,z are distinct. There are 24 meaningful ways to specify the right-hand sides of these five equations, and each of those functions can be expressed as a term in t.
There are a(4) meaningful ways to specify the right-hand sides of A000110(4)=15 analogous equations for a four-parameter function, and so on. - Don Knuth, Jul 07 2024
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