A360192 - OEIS

%I #27 Apr 01 2023 23:48:46

%S 1,13,157,1409,8237,35165,120809,351865,903921,2102065,4511365,

%T 9056021,17194093,31125005,54080341,90666045,147314445

%N Number of distinct means of nonempty subsets of points {(x,y)|1<=x<=n, 1<=y<=n}.

%e 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).

%e They can be visualized as follows:

%e Mark the set of points with "x" in a 2 X 2 matrix:

%e (xx)

%e (xx)

%e The points not in a particular subset are replaced with "."

%e For example, the subset {(1,1),(1,2)}

%e                    (x.)

%e is represented by: (x.)

%e The means for n=2 arise from the following subsets:

%e        (x.)

%e (1,1): (..)

%e -

%e        (.x)

%e (2,1): (..)

%e -

%e        (..)

%e (1,2): (x.)

%e -

%e        (..)

%e (2,2): (.x)

%e -

%e            (x.)    (.x)    (xx)

%e (3/2,3/2): (.x) or (x.) or (xx)

%e -

%e          (xx)

%e (3/2,1): (..)

%e -

%e          (..)

%e (3/2,2): (xx)

%e -

%e          (x.)

%e (1,3/2): (x.)

%e -

%e          (.x)

%e (2,3/2): (.x)

%e -

%e            (xx)

%e (4/3,4/3): (x.)

%e -

%e            (x.)

%e (4/3,5/3): (xx)

%e -

%e            (xx)

%e (5/3,4/3): (.x)

%e -

%e            (.x)

%e (5/3,5/3): (xx)

%Y Two-dimensional analog of A135342.

%K nonn,more

%O 1,2

%A _Nitai Sasson_, Jan 29 2023

%E a(10)-a(17) from _Zachary DeStefano_, Jan 29 2023