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There are two identities known as Catalan's identity. The first is F_n^2-F_(n+r)F_(n-r)=(-1)^(n-r)F_r^2, where F_n is a Fibonacci number. Letting r=1 gives Cassini's ...

A sequence a_1, a_2, ... such that the metric d(a_m,a_n) satisfies lim_(min(m,n)->infty)d(a_m,a_n)=0. Cauchy sequences in the rationals do not necessarily converge, but they ...

A figurate number of the form, CCub_n=n^3+(n-1)^3=(2n-1)(n^2-n+1). The first few are 1, 9, 35, 91, 189, 341, ... (OEIS A005898). The generating function for the centered cube ...

A figurate number in which layers of polygons are drawn centered about a point instead of with the point at a polygon vertex.

A fake knot (i.e., a knot equivalent to the unknot) created by tying a square knot, then looping one end twice through the knot such that when both ends are pulled, the knot ...

The inequality (j+1)a_j+a_i>=(j+1)i, which is satisfied by all A-sequences.

A node which is one graph edge further away from a given node in a rooted tree.

A Chu space is a binary relation from a set A to an antiset X which is defined as a set which transforms via converse functions.

A notation for large numbers due to Steinhaus (1999). In circle notation, is defined as n in n squares, where numbers written inside squares (and triangles) are interpreted ...

A partially ordered set P is a circle order if it is isomorphic to a set of disks ordered by containment.