In this work we introduce the triangular double sequences of arbitrary order given by linear recurrences, that generalize some well-known recurrences that appear in enumerative combinatorics. In particular, we focussed on triangular sequences generated by two double sequences and establish their relation with the solution of linear three-term recurrences. We show through some simple examples how these triangular sequences appear as essential components in the expression of some classical orthogonal polynomials and combinatorial numbers.

Peer Reviewed