Search Results for ""

The nth central fibonomial coefficient is defined as [2n; n]_F = product_(k=1)^(n)(F_(n+k))/(F_k) (1) = ...

Clark's triangle is a number triangle created by setting the vertex equal to 0, filling one diagonal with 1s, the other diagonal with multiples of an integer f, and filling ...

Two complex numbers x=a+ib and y=c+id are multiplied as follows: xy = (a+ib)(c+id) (1) = ac+ibc+iad-bd (2) = (ac-bd)+i(ad+bc). (3) In component form, ...

Pairs of partitions for a single number whose Ferrers diagrams transform into each other when reflected about the line y=-x, with the coordinates of the upper left dot taken ...

Let psi = 1+phi (1) = 1/2(3+sqrt(5)) (2) = 2.618033... (3) (OEIS A104457), where phi is the golden ratio, and alpha = lnphi (4) = 0.4812118 (5) (OEIS A002390). Define the ...

This is sometimes knows as the "bars and stars" method. Suppose a recipe called for 5 pinches of spice, out of 9 spices. Each possibility is an arrangement of 5 spices ...

A lobster graph, lobster tree, or simply "lobster," is a tree having the property that the removal of leaf nodes leaves a caterpillar graph (Gallian 2007). The numbers of ...

A fractal curve created from the base curve and motif illustrated above (Lauwerier 1991, p. 37). As illustrated above, the number of segments after the nth iteration is ...

The nth Monica set M_n is defined as the set of composite numbers x for which n|[S(x)-S_p(x)], where x = a_0+a_1(10^1)+...+a_d(10^d) (1) = p_1p_2...p_m, (2) and S(x) = ...

By way of analogy with the eban numbers, oban numbers are defined as numbers whose English names do not contain the letter "o" (i.e., "o" is banned). Note that this ...