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Polynomials O_n(x) that can be defined by the sum O_n(x)=1/4sum_(k=0)^(|_n/2_|)(n(n-k-1)!)/(k!)(1/2x)^(2k-n-1) (1) for n>=1, where |_x_| is the floor function. They obey the ...

An octic graph is a regular graph of degree eight. The numbers of simple octic graphs on n=9, 10, 11, ... nodes are 1, 6, 94, 10786, 3459386, ... (OEIS A014378). Examples are ...

Overdamped simple harmonic motion is a special case of damped simple harmonic motion x^..+betax^.+omega_0^2x=0, (1) in which beta^2-4omega_0^2>0. (2) Therefore ...

A test for the primality of Fermat numbers F_n=2^(2^n)+1, with n>=2 and k>=2. Then the two following conditions are equivalent: 1. F_n is prime and (k/F_n)=-1, where (n/k) is ...

A planar connected graph is a graph which is both planar and connected. The numbers of planar connected graphs with n=1, 2, ... nodes are 1, 1, 2, 6, 20, 99, 646, 5974, ...

An algorithm is said to be solvable in polynomial time if the number of steps required to complete the algorithm for a given input is O(n^k) for some nonnegative integer k, ...

A polyhedron having two polygons in parallel planes as bases and triangular or trapezoidal lateral faces with one side lying in one base and the opposite polyhedron vertex or ...

It is possible to find six points in the plane, no three on a line and no four on a circle (i.e., none of which are collinear or concyclic), such that all the mutual ...

An idealized computing machine consisting of a fixed set of data registers and set of instructions for operating on them. Register machines are also known as counter machines ...

The Robbins constant is the mean line segment length, i.e., the expected distance between two points chosen at random in cube line picking, namely Delta(3) = (1) = (2) = ...