Example: (1)Determine the number of ways in which postage of r cents can be pasted on an envelope using 1 1-cent, 1 2-cent, 1 4-cent, 1 8-cent and 1 16-cent stamps (2)Determine the number of ways in which postage of r cents can be pasted on an envelope using 2 1-cent, 3 2-cent and 2 5 cent stamps Assume that the order the stamps are pasted on does not matter Let ar be the number of ways in which postage of r cents. Then the generating function f(x)of this sequence a is (1)f(x)=(1+x)(1+x2)(1+x4)(1+x3)(1+x (2)f(x)=(1+x+x2)(1+x2+(x2)2+(x2)3)(1+x5+(x5)2)) 1+x+2x2+x3+2x4+2x5+3x6+3x7+2x8+2x9+2x10+3x1 +3x12+2x13+2x14+x15+2x16+x17+x18。▪ Example: (1)Determine the number of ways in which postage of r cents can be pasted on an envelope using 1 1-cent,1 2-cent, 1 4-cent, 1 8-cent and 1 16-cent stamps. ▪ (2)Determine the number of ways in which postage of r cents can be pasted on an envelope using 2 1-cent, 3 2-cent and 2 5- cent stamps. ▪ Assume that the order the stamps are pasted on does not matter. ▪ Let ar be the number of ways in which postage of r cents. Then the generating function f(x) of this sequence {ar } is ▪ (1)f(x)=(1+x)(1+x2 )(1+x4 )(1+x8 )(1+x16) ▪ (2)f(x)=(1+x+x2 )(1+x2+(x2 ) 2+(x2 ) 3 )(1+x5+(x5 ) 2 )） ▪ =1+x+2x2+x3+2x4+2x5+3x6+3x7+2x8+2x9+2x10+3x11 +3x12+2x13+ 2x14+x15+2x16+x17+x18