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$n$ -color partitions with weighted differences equal to minus two.

Agarwal, A.K., Balasubrananian, R. (1997)

International Journal of Mathematics and Mathematical Sciences

Neither $\prod_{k = 1}^{n} (4 k 2 + 1)$ nor $\prod_{k = 1}^{n} (2 k (k - 1) + 1)$ is a perfect square.

Fang, Jin-Hui (2009)

Integers

New formulae for $K_{i} (z)$ function.

Petojević, Aleksandar (2005)

Novi Sad Journal of Mathematics

Noncirculant Toeplitz matrices all of whose powers are Toeplitz

Kent Griffin, Jeffrey L. Stuart, Michael J. Tsatsomeros (2008)

Czechoslovak Mathematical Journal

Let $a$ , $b$ and $c$ be fixed complex numbers. Let $M_{n} (a, b, c)$ be the $n \times n$ Toeplitz matrix all of whose entries above the diagonal are $a$ , all of whose entries below the diagonal are $b$ , and all of whose entries on the diagonal are $c$ . For $1 \leq k \leq n$ , each $k \times k$ principal minor of $M_{n} (a, b, c)$ has the same value. We find explicit and recursive formulae for the principal minors and the characteristic polynomial of $M_{n} (a, b, c)$ . We also show that all complex polynomials in $M_{n} (a, b, c)$ are Toeplitz matrices. In particular, the inverse of $M_{n} (a, b, c)$ is a Toeplitz matrix when...