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A098358 Multiplication table of the triangular numbers read by antidiagonals. 9

%I

%S 1,3,3,6,9,6,10,18,18,10,15,30,36,30,15,21,45,60,60,45,21,28,63,90,

%T 100,90,63,28,36,84,126,150,150,126,84,36,45,108,168,210,225,210,168,

%U 108,45,55,135,216,280,315,315,280,216,135,55,66,165,270,360,420,441,420,360

%N Multiplication table of the triangular numbers read by antidiagonals.

%C 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

%H G. C. Greubel, <a href="/A098358/b098358.txt">Table of n, a(n) for the first 50 rows, flattened</a>

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

%F G.f.: x*y / ((1-x)^3 * (1-y)^3). - _Ralf Stephan_, Oct 27 2004

%e Triangle begins:

%e 1;

%e 3, 3;

%e 6, 9, 6;

%e 10, 18, 18, 10;

%e ...

%t 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 *)

%Y Cf. A003991, A098359, A098360, A098361.

%K nonn,tabl

%O 0,2

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

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Last modified May 7 12:34 EDT 2021. Contains 343650 sequences. (Running on oeis4.)