A360192 Number of distinct means of nonempty subsets of points {(x,y)|1<=x<=n, 1<=y<=n}.
1, 13, 157, 1409, 8237, 35165, 120809, 351865, 903921, 2102065, 4511365, 9056021, 17194093, 31125005, 54080341, 90666045, 147314445
Offset: 1
Examples
For n = 2 the a(2) = 13 means are (1, 1), (1, 2), (1, 3/2), (2, 1), (2, 2), (2, 3/2), (3/2, 1), (3/2, 2), (3/2, 3/2), (4/3, 4/3), (4/3, 5/3), (5/3, 4/3), (5/3, 5/3).
They can be visualized as follows:
Mark the set of points with "x" in a 2 X 2 matrix:
(xx)
(xx)
The points not in a particular subset are replaced with "."
For example, the subset {(1,1),(1,2)}
(x.)
is represented by: (x.)
The means for n=2 arise from the following subsets:
(x.)
(1,1): (..)
-
(.x)
(2,1): (..)
-
(..)
(1,2): (x.)
-
(..)
(2,2): (.x)
-
(x.) (.x) (xx)
(3/2,3/2): (.x) or (x.) or (xx)
-
(xx)
(3/2,1): (..)
-
(..)
(3/2,2): (xx)
-
(x.)
(1,3/2): (x.)
-
(.x)
(2,3/2): (.x)
-
(xx)
(4/3,4/3): (x.)
-
(x.)
(4/3,5/3): (xx)
-
(xx)
(5/3,4/3): (.x)
-
(.x)
(5/3,5/3): (xx)
Crossrefs
Two-dimensional analog of A135342.
Extensions
a(10)-a(17) from Zachary DeStefano, Jan 29 2023