

A190020


Number of obtuse triangles on a (n X n)grid (or geoboard)


4



0, 0, 24, 236, 1148, 3932, 10760, 25392, 53576, 103824, 188104, 322852, 529116, 835028, 1275360, 1893496, 2742208, 3886568, 5402448, 7381316, 9928860, 13168484, 17243896, 22319864, 28579720, 36237928, 45532720, 56732668
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OFFSET

1,3


COMMENTS

Place all bounding boxes of A280652 that will fit into the n X n grid in all possible positions, and the proper rectangles in two orientations: a(n) = sum(i=1..n, sum(j=1..i, k * (ni+1) * (nj+1) * A280652(i,j))) where k=1 when i=j and k=2 otherwise.  Lars Blomberg, Mar 02 2017


LINKS

Lars Blomberg, Table of n, a(n) for n = 1..10000
Barile, Margherita: MathWorld  Geoboard.
Weisstein, Eric W.: MathWorld  Obtuse Triangle.


FORMULA

a(n) = A045996(n)  A077435(n)  A190019(n).


CROSSREFS

Cf. A045996, A077435, A190019, A280652.
Sequence in context: A125387 A126545 A193168 * A213560 A159506 A081863
Adjacent sequences: A190017 A190018 A190019 * A190021 A190022 A190023


KEYWORD

nonn


AUTHOR

Martin Renner, May 04 2011


EXTENSIONS

Extended by Ray Chandler, May 04 2011


STATUS

approved



