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... > sequence > integer sequence > figurate number > polyhedral number > tetrahedral number

number > natural numbers > figurate number > polyhedral number > tetrahedral number

Terme préférentiel

tetrahedral number

Définition(s)

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, $Te n$ , is the sum of the first $n$ triangular numbers, that is,

${\\displaystyle Te_{n}=\\sum _{k=1}^{n}T_{k}=\\sum _{k=1}^{n}{\ rac {k(k+1)}{2}}=\\sum _{k=1}^{n}\\left(\\sum _{i=1}^{k}i\ ight)}$

The tetrahedral numbers are:

1, 4, 10, 20, 35, 56, 84, 120, 165, 220, ... (sequence A000292 in the OEIS)

(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Tetrahedral_number)

Concept(s) générique(s)

polyhedral number

Synonyme(s)

triangular pyramidal number

Traductions

nombre tétraédrique

français
nombre pyramidal triangulaire

URI

http://data.loterre.fr/ark:/67375/PSR-ZLW9BKRS-W

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