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

0,2

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

Links

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

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

Example

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

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 *)

Crossrefs

Cf. A003991, A098359, A098360, A098361.

Sequence in context: A379277 A110769 A093445 * A136289 A128012 A289143

Adjacent sequences: A098355 A098356 A098357 * A098359 A098360 A098361

Keyword

nonn,tabl

Author

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

Status

approved