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Let b(k) be the number of 1s in the binary expression of k, i.e., the binary digit count of 1, giving 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, ... (OEIS A000120) for k=1, 2, .... ...

An order-n Costas array is a permutation on {1,...,n} such that the distances in each row of the triangular difference table are distinct. For example, the permutation ...

The voter model is a simple mathematical model of opinion formation in which voters are located at the nodes of a network, each voter has an opinion (in the simplest case, 0 ...

A flexagon made by folding a strip into adjacent equilateral triangles. The number of states possible in a hexaflexagon is the Catalan number C_5=42.

An apodization function (also called a tapering function or window function) is a function used to smoothly bring a sampled signal down to zero at the edges of the sampled ...

A sequence s_n(x) is called a Sheffer sequence iff its generating function has the form sum_(k=0)^infty(s_k(x))/(k!)t^k=A(t)e^(xB(t)), (1) where A(t) = A_0+A_1t+A_2t^2+... ...

The vertical line test is a graphical method of determining whether a curve in the plane represents the graph of a function by visually examining the number of intersections ...

A busy beaver is an n-state, 2-color Turing machine which writes a maximum number Sigma(n) of 1s before halting (Rado 1962; Lin and Rado 1965; Shallit 1998). Alternatively, ...

Given a triangle center X=l:m:n, the line mnalpha+nlbeta+lmgamma=0, where alpha:beta:gamma are trilinear coordinates, is called the trilinear polar (Kimberling 1998, p. 38). ...

Let [arg(f(z))] denote the change in the complex argument of a function f(z) around a contour gamma. Also let N denote the number of roots of f(z) in gamma and P denote the ...