The following column numbers are given: 2, 43, 678, 131021 Then the nth number is______ (expressed by an algebraic expression containing n)

The following column numbers are given: 2, 43, 678, 131021 Then the nth number is______ (expressed by an algebraic expression containing n)

The molecules are continuous even numbers, the first number is 2, the second number is 4, the third number is 6 Let the denominator of the nth number be an, ∵ 2 = 21, ∵ A1 = 1, a2-a1 = 3-1 = 2 = 2 × 1, a3-a2 = 7-3 = 4 = 2 × 2, a4-a3 = 13-7 = 6 = 2 × 3, a5-a4 = 21-13 = 8 = 2 × 4 ，an-an-1=2（n-1），a1+a2-a1+a3-a2+a4-a3+a5-a4+… +an-an-1=1+2+2×1+2×2+2×3+2×4+… +2 (n-1), so an = 1 + 2 [1 + 2 + 3 + 4 +...] +(n-1)] = 1 + 2 × (1 + n − 1) (n − 1) 2 = n2-n + 1, so the nth number is 2nn2 − n + 1