Formula for binary sequences of length m with no n consecutive 1s? Formula for binary sequences of length $m$ with no $n$ consecutive $1$s?

I know The number of binary strings of length $m$ without consecutive $1$s is the Fibonacci number $F_{m+2}$.

But how about no $n$ consecutive $1$s?

Any help will be appreciated! Thank you
The same idea will work to make a recurrence.  To make a sequence of length $m$, you can take one of length $m-1$ and add a zero, one of length $m-2$ and add $01$, one of length $m-3$ and add $011$ on up to $m-n$ adding a zero and $n-1\ \ 1$'s
This formula should work-

Total sequences possible $=2^m=s(let)$;
Sequences with no $n$ consecutive $1$'s $= \frac{(m-n+1)(m-n+2)}2=t(let)$

Answer$=s-t$