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A190021 Number of acute triangles, distinct up to congruence, on a (n X n)-grid (or geoboard) 4
0, 0, 2, 8, 23, 51, 101, 179, 295, 460, 688, 988, 1382, 1876, 2495, 3258, 4191, 5298, 6613, 8166, 9973, 12065, 14472, 17208, 20341, 23873, 27838, 32282, 37238, 42734, 48840, 55573, 62973, 71067, 79934, 89640, 100172, 111613, 123959, 137336, 151842 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..41.

Barile, Margherita: MathWorld -- Geoboard.

Weisstein, Eric W.: MathWorld -- Acute Triangle.

FORMULA

a(n) = A028419(n) - A189979(n) - A190022(n).

EXAMPLE

For n = 3 the two acute triangles are:

*..   .*.

..*   *..

*..   ..*

MAPLE

Triangles:=proc(n) local TriangleSet, i, j, k, l, A, B, C; TriangleSet:={}: for i from 0 to n do for j from 0 to n do for k from 0 to n do for l from 0 to n do A:=i^2+j^2: B:=k^2+l^2: C:=(i-k)^2+(j-l)^2: if A^2+B^2+C^2<>2*(A*B+B*C+C*A) then TriangleSet:={op(TriangleSet), sort([sqrt(A), sqrt(B), sqrt(C)])}: fi: od: od: od: od: return(TriangleSet); end:

IsAcuteTriangle:=proc(T) if T[1]^2+T[2]^2>T[3]^2 and T[1]^2+T[3]^2>T[2]^2 and T[2]^2+T[3]^2>T[1]^2 then true else false fi: end:

a:=proc(n) local TriangleSet, AcuteTriangleSet, i; TriangleSet:=Triangles(n): AcuteTriangleSet:={}: for i from 1 to nops(TriangleSet) do if IsAcuteTriangle(TriangleSet[i]) then AcuteTriangleSet:={op(AcuteTriangleSet), TriangleSet[i]} fi: od: return(nops(AcuteTriangleSet)); end:

CROSSREFS

Cf. A028419, A189979, A190022.

Sequence in context: A178129 A203298 A161463 * A014285 A079460 A154144

Adjacent sequences:  A190018 A190019 A190020 * A190022 A190023 A190024

KEYWORD

nonn

AUTHOR

Martin Renner, May 04 2011

EXTENSIONS

a(21)--a(40) from Martin Renner, May 08 2011

STATUS

approved

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Last modified November 18 15:55 EST 2018. Contains 317323 sequences. (Running on oeis4.)