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C n is the number of noncrossing partitions of the set {1, ..., n}. A fortiori, C n never exceeds the n-th Bell number. C n is also the number of noncrossing partitions of the set {1, ..., 2n} in which every block is of size 2. C n is the number of ways to tile a stairstep shape of height n with n rectangles. Cutting across the anti-diagonal ...
A list of patterns that, when repeated to fill the cells of a Rule 30 automaton, repeat themselves after finitely many time steps. Frans Faase, 2003. Archived from the Original on 2013-08-08; Paving Mosaic Fractal. Basic introduction to the pattern of Rule 30 from the perspective of a LOGO software expert Olivier Schmidt-Chevalier.
The term can mean polygonal number; a number represented as a discrete r-dimensional regular geometric pattern of r-dimensional balls such as a polygonal number (for r = 2) or a polyhedral number (for r = 3). a member of the subset of the sets above containing only triangular numbers, pyramidal numbers, and their analogs in other dimensions. [1]
In mathematics, a pyramid number, or square pyramidal number, is a natural number that counts the stacked spheres in a pyramid with a square base. The study of these numbers goes back to Archimedes and Fibonacci. They are part of a broader topic of figurate numbers representing the numbers of points forming regular patterns within different shapes.
The machine will perform the following three steps on any odd number until only one 1 remains: Append 1 to the (right) end of the number in binary (giving 2n + 1); Add this to the original number by binary addition (giving 2n + 1 + n = 3n + 1); Remove all trailing 0 s (that is, repeatedly divide by 2 until the result is odd).
Step B: If the integer is between 1001 and one million, find a repeating pattern of 1, 2, or 3 digits that forms a 6-digit number that is close to the integer (leading zeros are allowed and can help you visualize the pattern). If the positive difference is less than 1000, apply Step A.
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The nth pentagonal number p n is the number of distinct dots in a pattern of dots consisting of the outlines of regular pentagons with sides up to n dots, when the pentagons are overlaid so that they share one vertex. For instance, the third one is formed from outlines comprising 1, 5 and 10 dots, but the 1, and 3 of the 5, coincide with 3 of ...