login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A190022 Number of obtuse triangles, distinct up to congruence, on a (n X n)-grid (or geoboard) 4
0, 0, 2, 12, 39, 95, 193, 355, 597, 943, 1426, 2071, 2904, 3977, 5306, 6956, 8963, 11370, 14225, 17587, 21515, 26053, 31310, 37282, 44061, 51785, 60436, 70127, 80939, 92952, 106267, 120982, 137124, 154841, 174225, 195366, 218394, 243457, 270505, 299749, 331441 (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 -- Obtuse Triangle.

FORMULA

a(n) = A028419(n) - A190021(n) - A189979(n).

EXAMPLE

For n = 3 the two obtuse 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:

IsObtuseTriangle:=proc(T) if T[1]^2+T[2]^2<T[3]^2 or T[1]^2+T[3]^2<T[2]^2 or T[2]^2+T[3]^2<T[1]^2 then true else false fi: end:

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

CROSSREFS

Cf. A028419, A189979, A190021.

Sequence in context: A026575 A048349 A009632 * A086602 A019006 A168057

Adjacent sequences:  A190019 A190020 A190021 * A190023 A190024 A190025

KEYWORD

nonn

AUTHOR

Martin Renner, May 04 2011

EXTENSIONS

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

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 19 05:29 EST 2018. Contains 317333 sequences. (Running on oeis4.)