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tetrahedral number : ウィキペディア英語版 | tetrahedral number
A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid with a triangular base and three sides, called a tetrahedron. The ''n''th tetrahedral number is the sum of the first ''n'' triangular numbers. The first ten tetrahedral numbers are: :1, 4, 10, 20, 35, 56, 84, 120, 165, 220, … == Formula ==
The formula for the ''n''-th tetrahedral number is represented by the 3rd rising factorial of ''n'' divided by the factorial of 3: : The tetrahedral numbers can also be represented as binomial coefficients: : Tetrahedral numbers can therefore be found in the fourth position either from left or right in Pascal's triangle.
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