DNA Sequence Alignment and Kings

🫧 Open on Bubbles This morning I wrote a post that included the central Delannoy numbers. The n th central Delannoy number D n counts the number of ways a king can move from one corner of a chessboard to the diagonally opposite corner without backtracking. The more general Delannoy numbers D m , n are the analogy for an m × n rectangular board, not necessarily square. D m , n is also the number of possible sequence alignments for a strand of DNA with m base pairs and a strand with n base pairs [1]. At each