cp's OEIS Frontend

A360192 Number of distinct means of nonempty subsets of points {(x,y)|1<=x<=n, 1<=y<=n}.

%I A360192 #27 Apr 01 2023 23:48:46
%S A360192 1,13,157,1409,8237,35165,120809,351865,903921,2102065,4511365,
%T A360192 9056021,17194093,31125005,54080341,90666045,147314445
%N A360192 Number of distinct means of nonempty subsets of points {(x,y)|1<=x<=n, 1<=y<=n}.
%e A360192 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 A360192 They can be visualized as follows:
%e A360192 Mark the set of points with "x" in a 2 X 2 matrix:
%e A360192 (xx)
%e A360192 (xx)
%e A360192 The points not in a particular subset are replaced with "."
%e A360192 For example, the subset {(1,1),(1,2)}
%e A360192                    (x.)
%e A360192 is represented by: (x.)
%e A360192 The means for n=2 arise from the following subsets:
%e A360192        (x.)
%e A360192 (1,1): (..)
%e A360192 -
%e A360192        (.x)
%e A360192 (2,1): (..)
%e A360192 -
%e A360192        (..)
%e A360192 (1,2): (x.)
%e A360192 -
%e A360192        (..)
%e A360192 (2,2): (.x)
%e A360192 -
%e A360192            (x.)    (.x)    (xx)
%e A360192 (3/2,3/2): (.x) or (x.) or (xx)
%e A360192 -
%e A360192          (xx)
%e A360192 (3/2,1): (..)
%e A360192 -
%e A360192          (..)
%e A360192 (3/2,2): (xx)
%e A360192 -
%e A360192          (x.)
%e A360192 (1,3/2): (x.)
%e A360192 -
%e A360192          (.x)
%e A360192 (2,3/2): (.x)
%e A360192 -
%e A360192            (xx)
%e A360192 (4/3,4/3): (x.)
%e A360192 -
%e A360192            (x.)
%e A360192 (4/3,5/3): (xx)
%e A360192 -
%e A360192            (xx)
%e A360192 (5/3,4/3): (.x)
%e A360192 -
%e A360192            (.x)
%e A360192 (5/3,5/3): (xx)
%Y A360192 Two-dimensional analog of A135342.
%K A360192 nonn,more
%O A360192 1,2
%A A360192 _Nitai Sasson_, Jan 29 2023
%E A360192 a(10)-a(17) from _Zachary DeStefano_, Jan 29 2023