21. Two non-decreasing sequences of non-negative integers have different first terms. Each sequence has the following property: from the third term onwards, each term is equal to the sum of the two preceding terms, and the seventh term of both sequences is $N$. Then the smallest possible value of $N$ is ( ).
(A) 55
(B) 89
(C) 104
(D) 144
( $\dot{E}) 273$
21. C.

If we denote two non-decreasing non-negative integer sequences as
$$
\begin{array}{l}
0,13,13,26,39,65,104, \cdots ; \\
8,8,16,24,40,64,104, \cdots
\end{array}
$$

In this case, the seventh term of both sequences is 104.
Next, we prove that 89 and 55 do not meet the conditions.
Let the first two terms of the sequence be \(a\) and \(b\) (\(a, b \in \mathbf{N}, a \leqslant b\)). Then the first seven terms are
$$
\begin{array}{l}
a, b, a+b, a+2 b, 2 a+3 b, 3 a+5 b, 5 a+8 b . \\
\text { If } 5 a+8 b=89 \Rightarrow b=\frac{89-5 a}{8} \geqslant a \\
\Rightarrow 13 a \leqslant 89 \Rightarrow a \leqslant 6 .
\end{array}
$$

By 8 I \((89-5 a) \Rightarrow 8 \mid(5 a-1)\)
$$
\Rightarrow a=5, b=8 \text {. }
$$

Therefore, there is only one sequence whose seventh term is 89.
Similarly, 55 does not meet the conditions.