How many strings of length $n$ with $m$ ones have no more than $k$ consecutive ones?
8645
A formula for bit strings with no $k$ consecutive $1$'s using generating functions
107010
How many elements of order $k$ are in $S_n$?
27840
What about $[n,k,7]$ binary perfect code? (Exercise from the book Fundamentals of Error Correcting Codes)
47799
Show that the number or $r$ combinations of $X$ which contain no consecutive integers is given by $\binom{n-r+1}{r}$
34452
In how many ways can you choose $k$ numbers out of $\{1,2,3,\dots,n\}$ so none of them is consecutive?
1405
Arrangements of a,a,a,b,b,b,c,c,c in which no three consecutive letters are the same
4221
Determining the number of bit strings of length n that contains no adjacent 0s
69410
Find subsequences of consecutive integers inside a list
57221
counting the number of elements in a conjugacy class of $S_n$
151466
Series of consecutive numbers (different lengths)
146491
Number of solutions of $x_1+x_2+\dots+x_k=n$ with $x_i\le r$
52043
Number of binary numbers with two consecutive zeros
62175
A general formula for $n$ distinguishable arrangements of length $\ell$ of a sequence of a given size?
90652
How long does a sequence need to be to be guaranteed to have a monotonic subsequence length k?
113980
Prove that a set of nine consecutive integers cannot be partitioned into two subsets with same product
52518
Infinite sequence of digits without consecutive repeating subsequenes
42795
Number of bit strings with 3 consecutive zeros or 4 consecutive 1s