A114491 Number of "ultrasweet" Boolean functions of n variables.

2, 3, 6, 17, 69, 407, 3808, 75165, 10607541

Offset: 0

Author

Don Knuth, Aug 17 2008, Oct 14 2008

Keywords

• nonn

Comments

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.

Examples

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

Crossrefs

Cf. A114302, A114303, A114572, A058673.