[seqfan] Re: 2D extension to A327474

[Richard J. Mathar]

I get 1, 7, 66, 383,.. for distinct centers of mass
of binary square nXn arrays of n=1,2,3,4...

The [x,y] means for n=1 are [0,0] (it does not matter whether
the cell is occupied or not, the mean is the same).
The [x,y] means for n=2 are 
{[1, 1], [1/2, 1/2], [0, 0], [0, 1/2], [1/2, 0], [1/2, 1], [1, 1/2]}

brute force Maple code:

# L is a list of sequentialized positions of 1, members in the range 0..n*m-1
# n is the number of rows, m the number of columns
# by modulo and remainder division of a member of L through m
# we get the x and y positions in the range 0..m-1 and 0..n-1
Aaux := proc(L,n,m)
        local xsum,ysum,lin,x,y ;
        xsum := 0 ;
        ysum := 0 ;
        for lin in L do
                x := modp(lin,m) ;
                y := floor(lin/m) ;
                xsum := xsum+x ;
                ysum := ysum+y ;
        end do:
        [xsum/m,ysum/n] ;
end proc:
A := proc(n)
        local xymean,n2,lpos,ones ;
        xymean := {} ;
        # nxn grid of 1's 2^(n^2) places ennumbered 0..2^(n^2-1)
        n2 := n^2 ;
        lpos := {seq(i,i=0..n2-1)} ;
        for ones in combinat[powerset](lpos) do
                {Aaux(ones,n,n)} ;
                xymean := xymean union % ;
        end do:
        print(xymean) ;
        nops(xymean) ;
end proc:
A(1) ;
A(2) ;
A(3) ;
A(4) ;

--
Richard J. Mathar https://www.mpia.de/~mathar