OFFSET
0,2
COMMENTS
An example of a 3-place formula in predicate logic is Ex Ay Ez P(x,y,z). The number of different formulas when x, y, z have to be different is A000629(3) = 26. When variables are allowed to coincide that means that there are 20 more formulas like, e.g., Ex Ay P(x,x,y) or Ex P(x,x,x).
a(n) is the number of vertices in a cocoon concertina n-cube and the sum of row n in A300695, which shows the number of vertices in that structure by rank. A000629(n) by comparison is the number of vertices in the convex concertina n-cube.
The differences with A000629, i.e., the numbers of formulas with coinciding variables, are 0, 0, 2, 20, 200, 2242, 28508, 408872, 6556894, 116547952, 2277942800, ...
LINKS
Tilman Piesk, Table of n, a(n) for n = 0..150
Tilman Piesk, List of all 46 formulas with 3 places
Tilman Piesk, Python code used to generate the sequence
FORMULA
a(0) = 1, a(n) = 2 * A083355(n) for n > 0.
CROSSREFS
KEYWORD
nonn
AUTHOR
Tilman Piesk, Mar 13 2018
STATUS
approved