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Tritriangular Number

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A number of the form

Tt_n=((n+2; 2); 2)=1/8n(n+1)(n+2)(n+3)

(Comtet 1974, Stanley 1999), where (n; k) is a binomial coefficient. The first few values are 3, 15, 45, 105, 210, 378, 630, ... (OEIS A050534). The generating function for the tritriangular numbers is

(3x)/((1-x)^5)=3x+15x^2+45x^3+104x^4+....
TritriangularLines

Given n lines in a plane, no two of which are parallel, and no three of which are concurrent, draw lines pairwise through their points of intersection. The number of new lines drawn is then Tt_(n-3) (Schmall 1915).

See also

Triangular Number

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References

Comtet, L. Problem 1. Advanced Combinatorics: The Art of Finite and Infinite Expansions, rev. enl. ed. Dordrecht, Netherlands: Reidel, p. 72, 1974.Schmall, C. N. "Problem 432." Amer. Math. Monthly 22, 130, 1915.Sloane, N. J. A. Sequence A050534 in "The On-Line Encyclopedia of Integer Sequences."Stanley, R. P. Problem 5.5, Case 2 in Enumerative Combinatorics, Vol. 2. Cambridge, England: Cambridge University Press, 1999.

Referenced on Wolfram|Alpha

Tritriangular Number

Cite this as:

Weisstein, Eric W. "Tritriangular Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TritriangularNumber.html

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