clearvars,clc

global series goodCt

series=''; goodCt=0;

addon;

goodCt

2^20

goodCt/2^20

2^20 / goodCt

function addon()

global series goodCt

  for new='01'

    saveseries=series;

    if length(series)<(new=='0')+1

      series=[series,new];

    else

      if new=='1' &&  series(end)=='1'

        continue

      end

      if new=='0' &&  isequal(series(end-1:end),'00')

        continue

      end

      series(end+1)=new;

    end

    if length(series)==20

      goodCt=goodCt+1;

    else

      addon;

    end

    series=saveseries;

  end

end

finds

goodCt =

   465

ans =

     1048576

ans =

      0.000443458557128906

ans =

          2255.00215053763

indicating that 465 out of the 2^20 = 1,048,576 possible sequences fit the criteria for a probability of   0.000443458557128906, or about 1 in 2255.