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A098358 Multiplication table of the triangular numbers read by antidiagonals. 9
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 (list; table; graph; refs; listen; history; text; internal format)
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: A164743 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

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Last modified February 23 18:54 EST 2018. Contains 299586 sequences. (Running on oeis4.)