文摘
The Schröder number SnSn counts the number of the lattice paths from (0,0)(0,0) to (n,n)(n,n), containing no point above the line y=xy=x and using only steps (1,0)(1,0), (0,1)(0,1) and (1,1)(1,1). We prove that Sn+2α≡Sn+2α+1(mod2α+2),where n≥1n≥1 and α≥1α≥1.