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A114491 Number of "ultrasweet" Boolean functions of n variables. 3
2, 3, 6, 17, 69, 407, 3808, 75165, 10607541 (list; graph; refs; listen; history; text; internal format)
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
EXAMPLE
For all n>1, a function like "x2" is counted in the present sequence but not in A114572.
CROSSREFS
Sequence in context: A325298 A361380 A073591 * A122939 A321399 A169974
KEYWORD
nonn
AUTHOR
Don Knuth, Aug 17 2008, Oct 14 2008
STATUS
approved

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)