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Search: id:A098358
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| A098358 |
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Multiplication table of the triangular numbers read by antidiagonals. |
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+0
5
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| 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; listen)
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OFFSET
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0,2
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COMMENT
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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
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FORMULA
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a(m,n) = m(m+1)n(n+1)/4.
G.f.: xy / [(1-x)^3 * (1-y)^3 ]. - Ralf Stephan, Oct 27 2004
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EXAMPLE
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1; 3,3; 6,9,6; 10,18,18,10; ...
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CROSSREFS
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Cf. A003991, A098359, A098360, A098361.
Sequence in context: A164743 A110769 A093445 this_sequence A136289 A128012 A058628
Adjacent sequences: A098355 A098356 A098357 this_sequence A098359 A098360 A098361
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KEYWORD
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nonn,tabl
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AUTHOR
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Douglas Stones (dssto1(AT)student.monash.edu.au), Sep 04 2004
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