How to create a matrix out of a radial distribution vector

I have a radial distribution vector and I would like to convert it into a matrix having the same distribution radially.

Example:

    V=[1 3 4 3 1]
    M=[0.1  0.7   1   0.7  0.1
       0.7  1.7   3   1.7  0.7
        1    3    4    3    1
       0.7  1.7   3   1.7  0.7
       0.1  0.7   1   0.7  0.1 ]

The values I've inserted are just an approximative interpolation to show the idea.

Is there a pre-made function for this or does it need to be coded, with the interpolation?

Thank you for the help!

[Iman Ansari]

V=[1 3 4 3 1];
M=[1 3 4 3 1]'*[1 3 4 3 1]./V(ceil(length(V)/2))

M =

    0.2500    0.7500    1.0000    0.7500    0.2500
    0.7500    2.2500    3.0000    2.2500    0.7500
    1.0000    3.0000    4.0000    3.0000    1.0000
    0.7500    2.2500    3.0000    2.2500    0.7500
    0.2500    0.7500    1.0000    0.7500    0.2500

[Jean Jacques]

Thanks for the fast answer. Unfortunately this is not what I am looking for. It kind of works for the kind of vector I proposed in example but not for a more complex vector. For example:

 V = [6 0 0 0 6]

 M = [0  4  6  4  0
      4  2  0  2  4
      6  0  0  0  6
      4  2  0  2  4
      0  4  6  4  0]

It is a circle from a radial distribution vector, with interpolated coefficients when not on the horizontal and vertical axis.