... electronic journal of combinatorics 17 (2010), #R160 16The Enumeration of Sequences with Restrictions on their Partial SumsStephen SuenDepartment of Mathematics and StatisticsUniversity of South ... up one,” and each “−t” meaning “go right one, g o down t.” We study the number of paths with conditions on their part ia l sums, on their number of crossings, crossingthe electronic journal of ... Spt+p+r= r.One common way to picture the sequences in relation to their partial sums is by consider-ing the sequences as paths {(j, Sj) : 0 j pt+p+r}, with each “+1” meaning “go rightone, go...