A050534 [Reference]

[Antreas P. Hatzipolakis]

ID Number: A050534
Sequence:  0,3,15,45,105,210,378,630,990,1485,2145,3003,4095,5460,7140,
            9180,11628,14535,17955,21945,26565,31878,37950,44850,52650,
            61425,71253,82215,94395,107880,122760,139128,157080,176715,
            198135,221445,246753
Name:      Tritriangular numbers: a(n)=binomial(binomial(n+2,2),2).
References L. Comtet, Advanced Combinatorics, Reidel, 1974,
Problem 1, page 72.
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999;
see Problem 5.5, case k=2.

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There are n straight lines in a plane, no two of which are parallel,
and no three of which are concurrent. Their points of interesection
being joined, show that the number of new lines drawn is
(1/8)n(n-1)(n-2)(n-3)

The American Mathematical Monthly 22(1915) 130 by C. N. Schmall


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