A189979 Number of right triangles, distinct up to congruence, on an n X n grid (or geoboard).

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

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