How to calculate the redundancy of a language
Not really, for example if your language has $m$ letters, and the letters are independent identically distributed then $H(X)=H(X_1,\ldots,X_N)=N H(X_1)$ where $H(X_1)$ is is the entropy of the single letter distribution $(p(1),\ldots,p(m)),$ where $P[X_k=u]=P[X_1=u]=p(u)$ for any $k\geq 1.$

This is because for independent random variables
$$
H(X_1,\ldots,X_n)=
$$
$$
=H(X_1)+H(X_2|X_1)+H(X_3|X_1 X_2)+\cdots+H(X_N|X_1X_2\cdots X_{N-1})=
$$
$$
=H(X_1)+H(X_2)+\cdots+H(X_N).
$$

So $X$ in that statement refers to the sequence of $N$ characters.

If your language is first order markov then
$$
H(X_1,\ldots,X_n)=
$$
$$
=H(X_1)+H(X_2|X_1)+H(X_3|X_1 X_2)+\cdots+H(X_N|X_1X_2\cdots X_{N-1})=
$$
$$
=H(X_1)+H(X_2|X_1)+H(X_3|X_2)+\cdots+H(X_N|X_{N-1})\geq (N-1)H(M).
$$
where $H(M)$ is the entropy of the Markov chain, i.e.,
$$
H(M)=\sum_{s\in S} \mu_s H(X_{n+1}|X_n=s)
$$
where $\mu_s$ is the steady state probability of being in the state $s$. Of course we need to assume a stationary Markov chain here.

See Shannon's classical paper Prediction and Entropy of Printed English (here )for a number of ways of calculating the entropy.