Zoom Maths Club - Numbers and Recurrent Relations - Dr Oleg Karpenkov

24th April 2021

In this talk, we will discuss several recurrent formulas that appear in the enumeration of various natural objects:

  1. Catalan Numbers (chords, brackets, chessboard rook travel);
  2. Markov Numbers (building solutions of Markov equation);
  3. Bernoulli-Euler Numbers (Bernoulli snakes and Euler snakes);
  4. Fibonacci Numbers (adding squares along the longest side);
  5. Numbers of $k$-combinations (Pascal's Triangle).

These formulas provide a fast way to compute these numbers.