The only cells that exist on row 2 are 'e' numbers that are "Congruent to 0 or 3 mod 4." according to oeis (A014601).

For a(n) functions, n = (x+1)/2 for odd, and x/2 for even.

From (11,2) up, I would assume b = a(n+2).

Some numbers have an offset of (n+1) or (n-1) on OEIS listings, I have included the term (n+1) and substituted it inside the formula of a(n).
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(0,2), Even Xs from 2

d : a(n) = n*(n+2) = (n+1)^2 - 1 (A005563).

a : a(n) = n^2, b : a(n) = (n+2)^2 = a(n+2).
Simply the squares.

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(3,2), Odd Xs from 1

d : a(n) = n*(n+1) = n^2 + n (A002378).
Oblong (or promic, pronic, or heteromecic) numbers.

a : a(n) = n^2 - n + 1, b : a(n+2) (A002061).
Central Polygonal numbers.

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(4,2) Even Xs from 2

d : a(n) = (n+1)^2. The squares.

a : a(n) = n^2 + 1, b : a(n+2) (A002522).

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(7,2), Odd Xs from 3

d : a(n) = n^2 + n + 1.

a : a(n) = n^2 - n + 2, b : a(n+2).

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(8,2), Even Xs from 2

d : a(n) = (n+1)^2 + 1 (A002522).

a : a(n) = n^2 + 2, b = a(n+2). (A059100).

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(11,2), from 3

d : a(n) = n^2 + n + 2 (A014206).

a : a(n) = n^2 - n + 3 .
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(12,2), from 2

d : a(n) = (n+1)^2 + 2 (A059100).

a : a(n) = n^2 + 3 (A117950).

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For the second row, we will define a variable as 'z' which is the same as '(n+1)', so basically ' z = n + 1 '.

As defined in the start of this text file, n = x/2 for even 'e' cells.

d = z^2 + (e-4)/4.

z = SQRT(d - (e-4)/4).

n = z - 1.

x = 2n

As we have seen in row 1, the even cell formula also works well with odd numbers of 'e', we will stick to this assumption for the rest of the rows.

These formulas defined above work well with all values where it is known that their 'n' is equal to 2, so this only works for 'n = 2'.