A tritriangular number is a number of the form
(Comtet 1974, Stanley 1999), where 
is a nonnegative integer
and 
is a binomial coefficient. The first few
values, for 
,
2, ..., are 3, 15, 45, 105, 210, 378, 630, ... (OEIS A050534).
The generating function for the tritriangular
numbers is
Given 
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 maximum number of distinct
new lines is 
, attained when no new line
contains more than two of the intersection
points (cf. Schmall 1915, p. 130).
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. https://doi.org/10.2307/2973734.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 Resource. https://mathworld.wolfram.com/TritriangularNumber.html
Subject classifications
