Summary: The binomial interpolated transform of a sequence is a generalization of the well-known binomial transform. We examine a Pascal-like triangle, on which a binomial interpolated transform works between the left and right diagonals, focusing on binary recurrences. We give the sums of the elements in rows and in rising diagonals, and we define two special classes of these arithmetical triangles.

11B37, 11B39, 11B65, 11B75

binomial operator, binomial transform, binomial interpolated transform, recurrence sequence