Forward difference table

Here h = 1. A forward difference table lists Δyᵢ = yᵢ₊₁ − yᵢ, then Δ²yᵢ = Δyᵢ₊₁ − Δyᵢ, and so on, until the differences vanish.

Working:

Δf: 9−2 = 7,  28−9 = 19,  65−28 = 37,  126−65 = 61,  217−126 = 91
Δ²f: 19−7 = 12,  37−19 = 18,  61−37 = 24,  91−61 = 30
Δ³f: 18−12 = 6,  24−18 = 6,  30−24 = 6
Δ⁴f: 0, 0, ...

The third differences are constant (= 6) and the fourth differences are zero, so f(x) is a cubic polynomial (indeed f(x) = x³ + 1). The first row (2, 7, 12, 6, 0, 0) is the set of values used by Newton's forward formula.