A334970 Sum of the values of the "shortest + middle - longest" side lengths of all primitive Heronian triangles with perimeter A096468(n).

2, 4, 2, 4, 2, 12, 6, 14, 4, 6, 18, 18, 6, 2, 22, 6, 16, 26, 2, 2, 4, 8, 38, 36, 8, 88, 46, 26, 20, 6, 44, 12, 8, 20, 72, 30, 64, 6, 28, 44, 66, 6, 50, 62, 24, 160, 18, 14, 20, 36, 4, 72, 2, 34, 28, 70, 142, 164, 48, 100, 10, 36, 82, 94, 86, 48, 124, 122, 46, 24, 108, 18, 34

Offset: 1

Author

Wesley Ivan Hurt, May 17 2020

Keywords

• nonn

Comments

a(n) is the excess length on the shortest and/or middle sides of all the primitive Heronian triangles with perimeter A096468(n) to avoid becoming degenerate triangles whose longest side is equal to the longest side of each primitive Heronian triangle.

Examples

			a(1) = 2; there is one primitive Heronian triangle with perimeter A096468(1) = 12, which is [3,4,5] and 3 + 4 - 5 = 2.
a(6) = 12; there are two primitive Heronian triangles with perimeter A096468(6) = 36, [9,10,17] and [10,13,13]. Then (9 + 10 - 17) + (10 + 13 - 13) = 2 + 10 = 12.
		

Links

• Eric Weisstein's World of Mathematics, Heronian Triangle
• Wikipedia, Heronian triangle
• Wikipedia, Integer Triangle

Crossrefs

Cf. A096468.