Weiqi Jiang

Exact Dyadic Periods for a Family of Generalized Central Trinomial Coefficients

We study the generalized central trinomial family B(n; u, v) = Σ from j = 0 to n of C(n, j)² uⁿ⁻ʲvʲ for integral parameters u and v. For parameters of opposite parity, for every k ≥ 4 and all n ≥ 0, B(n + 2ᵏ⁻²; u, v) ≡ B(n; u, v) modulo 2ᵏ; the shift 2ᵏ⁻² is a period from n = 0....