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.
Read more about this topic: Tetrahedral Number
Famous quotes containing the word formula:
“In the most desirable conditions, the child learns to manage anxiety by being exposed to just the right amounts of it, not much more and not much less. This optimal amount of anxiety varies with the childs age and temperament. It may also vary with cultural values.... There is no mathematical formula for calculating exact amounts of optimal anxiety. This is why child rearing is an art and not a science.”
—Alicia F. Lieberman (20th century)
“I feel like a white granular mass of amorphous crystalsmy formula appears to be isomeric with Spasmotoxin. My aurochloride precipitates into beautiful prismatic needles. My Platinochloride develops octohedron crystals,with a fine blue florescence. My physiological action is not indifferent. One millionth of a grain injected under the skin of a frog produced instantaneous death accompanied by an orange blossom odor.”
—Lafcadio Hearn (18501904)
“For the myth is the foundation of life; it is the timeless schema, the pious formula into which life flows when it reproduces its traits out of the unconscious.”
—Thomas Mann (18751955)