Compositions by 1 and 2 of compositions of n #of (1,2,...,xk) with summands from for some k≤m {1,2} x1十·+xk=n x∈{1,2} an an-1 an-2 a0=1a1=1 Case.I Xk=1 x1+··+ck-1=九-1 Case.2 k =2 1+..+xk-1=n-2# of compositions of n with summands from {1,2} xi ￾ {1, 2} Case.1 Case.2 xk = 1 xk = 2 x1 + ··· + xk￾1 = n ￾ 1 x1 + ··· + xk￾1 = n ￾ 2 Compositions by 1 and 2 for some k ￾ n # of (x1, x2,...,xk) x1 + ··· + xk = n an = an￾1 + an￾2 a0 = 1 a1 = 1