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A190019 Number of acute triangles on a (n X n)-grid (or geoboard). 4
0, 0, 8, 80, 404, 1392, 3880, 9208, 19536, 38096, 69288, 119224, 196036, 310008, 474336, 705328, 1023216, 1451904, 2020232, 2762848, 3719420, 4937200, 6469424, 8378184, 10734664, 13618168, 17119288, 21338760, 26390452, 32400592, 39508656, 47870200, 57655752 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Place all bounding boxes of A280653 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) * A280653(i,j) where k=1 when i=j and k=2 otherwise. - Lars Blomberg, Feb 26 2017

LINKS

Lars Blomberg, Table of n, a(n) for n = 1..5000

Margherita Barile, Geoboard.

Eric Weisstein's World of Mathematics, Acute Triangle.

FORMULA

a(n) = A045996(n) - A077435(n) - A190020(n).

CROSSREFS

Cf. A045996, A077435, A280653.

Sequence in context: A100431 A173116 A102698 * A055346 A159710 A271555

Adjacent sequences:  A190016 A190017 A190018 * A190020 A190021 A190022

KEYWORD

nonn

AUTHOR

Martin Renner, May 04 2011

EXTENSIONS

Extended by Ray Chandler, May 04 2011

More terms from Lars Blomberg, Feb 26 2017

STATUS

approved

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Last modified November 16 12:40 EST 2018. Contains 317272 sequences. (Running on oeis4.)