A098358 Multiplication table of the triangular numbers read by antidiagonals.

1, 3, 3, 6, 9, 6, 10, 18, 18, 10, 15, 30, 36, 30, 15, 21, 45, 60, 60, 45, 21, 28, 63, 90, 100, 90, 63, 28, 36, 84, 126, 150, 150, 126, 84, 36, 45, 108, 168, 210, 225, 210, 168, 108, 45, 55, 135, 216, 280, 315, 315, 280, 216, 135, 55, 66, 165, 270, 360, 420, 441, 420, 360

Offset: 0

Author

Douglas Stones (dssto1(AT)student.monash.edu.au), Sep 04 2004

Keywords

• nonn
• tabl

Comments

The number of rectangles to be found in a grid of size X by y. For example a(2, 2) = 9 since a 2 x 2 grid contains one rectangle of size 2 X 2, 4 of size 1 X 2 and 4 of size 1 X 1. - Hugo van der Sanden, May 24 2007

Examples

			Triangle begins:
   1;
   3,  3;
   6,  9,  6;
  10, 18, 18, 10;
  ...
		

Links

• G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Crossrefs

Cf. A003991, A098359, A098360, A098361.

Programs

Mathematica

a[n_, k_] := Binomial[k + 1, 2]*Binomial[n + 1, 2]; Table[a[n - k + 1, k], {n, 10}, {k, n, 1, -1}] // Flatten (* G. C. Greubel, Jul 22 2017 *)

Formula

a(m,n) = m*(m+1)*n*(n+1)/4.

G.f.: x*y / ((1-x)^3 * (1-y)^3). - Ralf Stephan, Oct 27 2004