Integer grids as integer sequences generators
Abstract
We investigate equidistant integer grids and semigrids as integer sequence generators. Equidistant integer grids are made of arithmetic sequences placed into rows and columns. Among others, partial sums of their diagonal elements give polygonal and second polygonal numbers. Further, sequences of row sums in integer semigrids satisfy specific recurrence relations. We analyze such sequences in detail for Pascals’ triangle semigrid obtained in two ways: only by shifting columns and by stretching and shifting columns.Keywords
arithmetic progression, integer grids, integer semigrids, recurrence relations