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A189979 Number of right triangles, distinct up to congruence, on an n X n grid (or geoboard). 5
0, 1, 4, 9, 17, 26, 39, 53, 71, 91, 114, 136, 169, 197, 231, 267, 310, 346, 397, 437, 492, 548, 606, 654, 729, 791, 858, 928, 1007, 1071, 1173, 1241, 1333, 1423, 1509, 1600, 1728, 1814, 1912, 2015, 2144 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

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

EXAMPLE

For n=3 the four right 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:

IsRectangularTriangle:=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, RectangularTriangleSet, i; TriangleSet:=Triangles(n): RectangularTriangleSet:={}: for i from 1 to nops(TriangleSet) do if IsRectangularTriangle(TriangleSet[i]) then RectangularTriangleSet:={op(RectangularTriangleSet), TriangleSet[i]} fi: od: return(nops(RectangularTriangleSet)); end:

CROSSREFS

Cf. A028419, A077435.

Sequence in context: A161320 A170879 A134578 * A272718 A301255 A009851

Adjacent sequences:  A189976 A189977 A189978 * A189980 A189981 A189982

KEYWORD

nonn,more

AUTHOR

Martin Renner, May 03 2011

EXTENSIONS

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

STATUS

approved

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Last modified October 20 05:31 EDT 2018. Contains 316378 sequences. (Running on oeis4.)