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A189978 Number of isosceles triangles, distinct up to congruence, on a (n X n)-grid (or geoboard). 7
0, 1, 5, 11, 22, 35, 53, 70, 100, 126, 159, 188, 237, 276, 328, 372, 439, 491, 564, 623, 706, 775, 859, 931, 1049, 1129, 1231, 1323, 1448, 1540, 1674, 1772, 1928, 2041, 2183, 2301, 2483, 2602, 2758, 2898, 3095 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

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

Alec Jones, Examples for n = 1 to 5

Alec Jones, Example for n = 24

EXAMPLE

For n=3 the five isosceles 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:

IsIsoscelesTriangle:=proc(T) if T[1]=T[2] or T[1]=T[3] or T[2]=T[3] then true else false fi: end:

a:=proc(n) local TriangleSet, IsoscelesTriangleSet, i;

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

CROSSREFS

Cf. A028419, A186434.

Sequence in context: A069097 A222548 A024921 * A192761 A152533 A228485

Adjacent sequences:  A189975 A189976 A189977 * A189979 A189980 A189981

KEYWORD

nonn,more

AUTHOR

Martin Renner, May 03 2011

EXTENSIONS

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

STATUS

approved

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Last modified December 19 11:05 EST 2018. Contains 318246 sequences. (Running on oeis4.)