DANBURY - The city’s effort to capitalize on economic opportunities of mutual interest with neighboring parts of New York has expanded to Western Connecticut State University, which is recruiting students from across the border by offering in-state tuition rates. WCSU’s border initiative, which includes an advertising campaign and a plan to send recruiters to New York high schools, is part of a larger effort by City Hall to exploit common ground between one of Connecticut’s fastest-growing cities and Putnam County, a six-town suburban county of 100,000 that is trying to encourage economic development.