Compositions by 1 and 2 of compositions of n #of(x1,x2,.,ck） with summands from for some k≤m {1,2} c1+··十ck=n x∈{1,2} Fn Fn-1+Fn-2 F0=0F1=1 Case.I Ck=1 x1+···+2ck-1=m-1 Case.2 xk=2x1+·+xk-1=n-2# of compositions of n with summands from {1,2} xi ￾ {1, 2} Fn Case.1 Case.2 xk = 1 xk = 2 x1 + ··· + xk￾1 = n ￾ 1 x1 + ··· + xk￾1 = n ￾ 2 = Fn￾1 + Fn￾2 F0 = 0 F1 = 1 Compositions by 1 and 2 for some k ￾ n # of (x1, x2,...,xk) x1 + ··· + xk = n