A331011 16 * squared area of triangles with integer sides i <= j <= k, such that more than one ordered triple of sides produces the same area.

63, 495, 675, 768, 1008, 1071, 1280, 1575, 2304, 2499, 2835, 2880, 2975, 3135, 3456, 3591, 4095, 4275, 4455, 4608, 4928, 5103, 5760, 5775, 6615, 6656, 6831, 6975, 7040, 7488, 7875, 7920, 8064, 8415, 8448, 8463, 8775, 8855, 8960, 9135, 9216, 9600, 9984, 10535

Offset

1,1

Links

Table of n, a(n) for n=1..44.

Example

a(1) = 63: triangles (1,4,4) and (2,2,3) both have squared area 3.9375 = 63/16. All smaller squared area values A(i,j,k) correspond to unique triples of side lengths: A(1,1,1) = 0.1875 = 3/16, A(1,2,2) = 0.9375 = 15/16, A(1,3,3) = 2.1875 = 35/16, A(2,2,2) = 3 = 48/16.
a(2) = 495: A(2,6,7) = A(3,4,4) = 30.9375 = 495/16.
a(8) = 1575: A(2,11,12) = A(3,8,10) = A(4,5,6) = 98.4375 = 1575/16.
a(23) = 5760: A(2,19,19) = A(3,13,14) = A(6,7,7) = A(6,7,11) = 360 = 5760/16.

Crossrefs

Subset of A317182.

Sequence in context: A075934 A075939 A075935 * A283931 A038858 A307527

Adjacent sequences: A331008 A331009 A331010 * A331012 A331013 A331014

Keyword

nonn

Author

Hugo Pfoertner, Jan 06 2020

Status

approved