SEATTLE — Fall enrollment is up at Washington’s public universities this fall. Most of the increase comes from students who decided to stay in school rather than seeking their fortunes elsewhere in a down economy. The University of Washington in Seattle, Western Washington University and The Evergreen State College are reporting only slight increases in their student count. While Washington State, UW Bothell, Eastern Washington and Central Washington all report record enrollment increases. The University of Washington has about 700 more students at its Seattle campus this year when compared to fall 2008. Most of the increase is in graduate students. Freshman enrollment is down several hundred, and transfer numbers remain about the same. Enrollment at the four campuses of Washington State University is up 830 students.