Some da capo directed power-sequence image terraces with n an odd prime power Original Research Article

A terrace for image is a particular type of sequence formed from the n elements of image. For n odd, many procedures are available for constructing power-sequence terraces for image; each such terrace may be partitioned into segments one of which contains merely the zero element of image, whereas each other segment is either (a) a sequence of successive powers of a non-zero element of image or (b) such a sequence multiplied throughout by a constant. We now extend this idea by using power-sequences in image to produce some terraces for image where n is an odd prime power satisfying image or 3 (mod 8). Each terrace now consists of a sequence of segments, one containing merely the element 0 and another merely containing the element n, the remaining segments each being of type (a) or (b) above with each of its distinct entries i from image evaluated so that image. The terraces constructed are da capo directed terraces, i.e. each terrace image has image) for all i satisfying image where image.