Sequences

Second column of A027496.

Third column of A027496.

First column of A027497.

Second column of A027497.

Third column of A027497.

Square of the lower triangular normalized partition matrix.

Cube of the lower triangular normalized partition matrix.

4th power of the lower triangular normalized partition matrix.

First diagonal of A027516.

Second diagonal of A027516.

Third diagonal of A027516.

First diagonal of A027517.

Second diagonal of A027517.

Third diagonal of A027517.

First diagonal of A027518.

Second diagonal of A027518.

Third diagonal of A027518.

First column of A027516.

Second column of A027516.

Third column of A027516.

First column of A027517.

Second column of A027517.

Third column of A027517.

First column of A027518.

Second column of A027518.

Third column of A027518.

Square of the lower triangular normalized Eulerian number matrix.

Cube of the lower triangular normalized Eulerian number matrix.

4th power of the lower triangular normalized Eulerian number matrix.

Second diagonal of A027537.

Third diagonal of A027537.

Second diagonal of A027538.

Third diagonal of A027538.

Second diagonal of A027539.

Third diagonal of A027539.

First column of A027537.

Second column of A027537.

Third column of A027537.

First column of A027538.

Second column of A027538.

Third column of A027538.

First column of A027539.

Second column of A027539.

Third column of A027539.

Triangle of binomial coefficients C(-n,k).

Unbalanced strings of length n.

Number of 3-balanced strings of length n: let d(S)= #(1)'s in S - #(0)'s, then S is k-balanced if every substring T has -k<=d(T)<=k; here k=3.

Number of 3-unbalanced strings of length n (= 2^n - A027557(n)).

Number of 4-balanced strings of length n: let d(S)= #(1)'s in S - #(0)'s, then S is k-balanced if every substring T has -k<=d(T)<=k; here k=4.

Number of 5-balanced strings of length n: let d(S)= #(1)'s in S - #(0)'s, then S is k-balanced if every substring T has -k<=d(T)<=k; here k=5.