We worked with analogs of the Fibonacci sequence. This leads to the question of a more general case . The construction of these formulas from basic identities serves as their proof.
Additional proof is given for the formula, since it appears within the formulas for and .
Mathematica is used to carry out large computations and to verify formulas. Introduction We are investigating fibonacci numbers and other sequences inspired by the fibonacci numbers. A few examples may be needed for clarification. The fifth fibonacci number would be denoted since it is the fifth number in a sequence created by summing the previous 2 terms. The formula can be constructed and explained best using Glaister's Investigative approach.