Rhomboidal numbers and arithmetical rhombi (Q2742964)

On the basis of a second-order recurrence relation, which is symmetric with respect to the right \((n)\) and left \((m)\) lines of the arithmetical rhombus, a set of combinatorial numbers \(\left\langle\thickfrac\thickness{0}{n}{m}\right\rangle\), called rhomboidal numbers, is constructed. The basis of the fractal geometry of rhomboidal numbers \(\mod 2\) is worked out, and the problem of distribution of rhomboidal numbers \(\left\langle\thickfrac \thickness{0}{n}{m}\right \rangle\bmod 2\) in the arithmetical rhombi \(R_n\), for any natural number \(n\), is solved.