0,1

A Boolean function is ultrasweet if it is sweet (see A114302) under all permutations of the variables.

Two students, Shaddin Dughmi and Ian Post, have identified these functions as precisely the monotone Boolean functions whose prime implicants are the bases of a matroid, together with the constant function 0. This explains why a[n]=A058673[n]+1.

For all n>1, a function like "x2" is counted in the present sequence but not in A114572.

Cf. A114302, A114303, A114572, A058673.

Sequence in context: A018284 A078344 A024498 this_sequence A122939 A003183 A131788

Adjacent sequences: A114488 A114489 A114490 this_sequence A114492 A114493 A114494

nonn

D. E. Knuth, Aug 17 2008, Oct 14 2008