CIRCULAR AVOIDING SEQUENCES WITH PRESCRIBED SUM

For given positive integers x, n, and s an x-avoiding circular sequenc e (of positive integers) of length n and sum s has no set of consecuti ve terms summing to x, even if wraparound is allowed. A necessary and sufficient condition for the existence of such a sequence is obtained. An effective method to construct avoiding sequences is given. For the cases of most interest the number of avoiding sequences is found.