A Visual Approach to Weighted Diagonal Sums in Pascal’s Triangle

SummaryIt is well known that Fibonacci numbers appear as diagonal sums in Pascal’s triangle. In this paper, we explore how visual arguments based on Pascal’s rule for binomial coefficients can be used to show that other recursive sequences, such as the Jacobsthal numbers, can also be expressed as weighted diagonal sums in Pascal’s triangle. Furthermore, we apply this visual representation to prove properties of such sequences.