How do I generate a vector of random integers without repeats and with j+2 constraints?

I need to generate a vector of 64 random integers with the following constraints:

1. The number have to be between 1 and 9 (excluding 4);
2. There can be no j+1 repeats (i.e. [5 6 6]);
3. There have to be 16 j+2 repeats (i.e. [5 6 5]);

I can get constraints 1 & 2 to work alone as well as constraint 3 alone using while. However, when I include them together (see below), the script just continues and doesn't give an output.

clear all, clc

x = randi([1,8],64,1); 

x(x==4) = 9;             % converts all 4s into 9s 

y = diff(x); y2 = [9; y]; x2 = [x y2]; % repeat identifier column

while any(diff(x)==0)
    while size(find(([x; 999; 999]-[999; 999; x])==0),1) ~=16
        x = randi([1,8],64,1);
        x(x==4) = 9;
    end
end

x

length(find(diff(x)==0)) % gives the number of j+1 repeats

Any suggestions on where to go from here would be excellent.

Just so you know where I'm going with this, once I've accomplished this, I would like to add two further constraints:

4. I would like to restrict the probability of each integer to .125 (i.e. each integer would be included 8 times);

5. There would be 8 j+2 repetitions involving each integer.

Answer 1

[Paulo Silva]

%constraints 1 2 3
x=[];
while(numel(x)~=64) %get more values until we get enough
    c=0;
    while(c==0)
        x = randi([1,8],80,1);
        x(x==4) = 9; %substitute 4 by 9
        x(diff(x)==0)=[] %remove repeated values
        %find 16 values repeated with other in the middle
        for a=1:numel(x)
            for b=1:2:numel(x)-2
                if (x(b)==x(b+2))
                    c=c+1;
                end
                if (c==16)
                    break
                end
            end
        end
    end
end

[Todd Flanagan]

Devin says, "Paulo, your script meets constraints #1 and #2 but it doesn't meet #3, it consistently yields fewer than 16 j+2 repeats."

Answer 2

[Matt Fig]

Some of your constraints would seem to be exclusive at first read. Here is an attempt at all 5:

N = [1 2 3 5 6 7 8 9];
A = zeros(4,16);

for ii = 1:4:13
    A(:,ii:ii+3) = repmat(reshape(N(randperm(8)),2,4),2,1);
end

B = randperm(16);
Vec = zeros(1,64);
Vec(1:4) = A(:,B(1));  % This is our resultant vector.
cnt = 5;

for ii = B(2:16)
    T = A(:,ii);
    if T(1) == Vec(cnt-1)
        T = T(4:-1:1);
    end
    Vec(cnt:cnt + 3) = T;
    cnt = cnt + 4;
end

[Todd Flanagan]

Devin says, "Matt, your script is very helpful as well. You are correct that my constraints are exclusive. I made a mistake - constraint #5 should be that there should be 2 j+2 repetitions involving each integer, resulting in a total of 16, as in constraint #3.

At present, your script doesn't appear very random but I imagine this is probably because you were trying to meet (my mistaken) constraint #5. If it reduced down to 2 j+2 repetitions per integer, it may work out."