cp's OEIS Frontend

A098358 Multiplication table of the triangular numbers read by antidiagonals.

%I A098358 #11 Jul 23 2017 21:41:51
%S A098358 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 A098358 100,90,63,28,36,84,126,150,150,126,84,36,45,108,168,210,225,210,168,
%U A098358 108,45,55,135,216,280,315,315,280,216,135,55,66,165,270,360,420,441,420,360
%N A098358 Multiplication table of the triangular numbers read by antidiagonals.
%C A098358 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 A098358 G. C. Greubel, <a href="/A098358/b098358.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%F A098358 a(m,n) = m*(m+1)*n*(n+1)/4.
%F A098358 G.f.: x*y / ((1-x)^3 * (1-y)^3). - _Ralf Stephan_, Oct 27 2004
%e A098358 Triangle begins:
%e A098358    1;
%e A098358    3,  3;
%e A098358    6,  9,  6;
%e A098358   10, 18, 18, 10;
%e A098358   ...
%t A098358 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 A098358 Cf. A003991, A098359, A098360, A098361.
%K A098358 nonn,tabl
%O A098358 0,2
%A A098358 Douglas Stones (dssto1(AT)student.monash.edu.au), Sep 04 2004