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

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

Offset

0,1

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.

Links

Table of n, a(n) for n=0..8.

Example

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

Crossrefs

Cf. A114302, A114303, A114572, A058673.

Sequence in context: A325298 A361380 A073591 * A122939 A321399 A169974

Adjacent sequences: A114488 A114489 A114490 * A114492 A114493 A114494

Keyword

nonn

Author

Don Knuth, Aug 17 2008, Oct 14 2008

Status

approved