A316853 Areas of all nondegenerate integer triangles, T, expressed as 16*area(T)^2. a(n) is for the triangle with sides A316841(n, 1..3).

3, 15, 48, 63, 35, 128, 243, 135, 320, 63, 240, 495, 768, 275, 231, 576, 975, 99, 384, 819, 1344, 1875, 455, 1008, 351, 896, 1575, 2304, 143, 560, 1215, 2048, 2975, 3888, 735, 675, 1536, 2499, 495, 1280, 2295, 3456, 4655, 195, 768, 1683, 2880, 4275

Offset: 1

Author

N. J. A. Sloane, Jul 23 2018

Keywords

• nonn

Comments

The squared area of an integer triangle is necessarily a multiple of 1/16.

Links

• Lars Blomberg, Table of n, a(n) for n = 1..3000
• Eric Weisstein's World of Mathematics, Triangle Area.

Crossrefs

Cf. A316841, A316842, A316843, A316844, A316845, A316851.

Formula

a(n) = 16*s*(s-a)*(s-b)*(s-c) where s = A316851(n)/2, and a,b,c are A316843(n), A316844(n), A316845(n).

Extensions

Name edited by Peter Munn, May 10 2025