Add Up Those (a,b) Pair Contributions to the Total Integer Density

-- the cardinalities in the rows of sets (varying a but sharing b) of the 2^a*3^b*n+c formulas exhibit the Fibonacci series or its 2ⁱ multiples

-- this provides a way to determine that all integers are present in the predecessor tree

      -- the known sum(F(i)/2⁽ⁱ⁺¹⁾,i=1..infinity)=1      where F(i) are the Fibonacci numbers
      -- make proper allowance for offsets and multiples among the F(i) in the cardinality table
      -- whence the total density will be the sum(2ⁱ/3⁽ⁱ⁺²⁾,i=0..infinity) or 1/2

-- 1/2 of all the integers is exactly the density required to cover all odd integers.

-- if one considers the powers-of-2 multiples of every odd number on the binary predecessor tree, and sums their densities, they total 1/2 also.

-- thus every positive integer, half even and half odd, is accounted for in a fine-grained analysis