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 A190020 Number of obtuse triangles on an n X n grid (or geoboard). 6
 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 (list; graph; refs; listen; history; text; internal format)
 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 * (n-i+1) * (n-j+1) * A280652(i,j) where k=1 when i=j and k=2 otherwise. - Lars Blomberg, Mar 02 2017 According to Langford (p. 243), the leading order is (97/150 + Pi/40)*C(n^2,3). See A093072. - Michael R Peake, Jan 15 2021 LINKS Lars Blomberg, Table of n, a(n) for n = 1..10000 Margherita Barile, MathWorld -- Geoboard. Eric Langford, A problem in geometric probability, Mathematics Magazine, Nov-Dec, 1970, 237-244. Eric Weisstein's World of Mathematics, Obtuse Triangle. FORMULA a(n) = A045996(n) - A077435(n) - A190019(n). CROSSREFS Cf. A045996, A077435, A093072, 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

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Last modified December 10 02:09 EST 2022. Contains 358712 sequences. (Running on oeis4.)