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

1,1

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.

Links

Table of n, a(n) for n=1..73.

Eric Weisstein's World of Mathematics, Heronian Triangle

Wikipedia, Heronian triangle

Wikipedia, Integer Triangle

Example

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.

Crossrefs

Cf. A096468.

Sequence in context: A366261 A086152 A194577 * A274708 A280638 A333725

Adjacent sequences: A334967 A334968 A334969 * A334971 A334972 A334973

Keyword

nonn

Author

Wesley Ivan Hurt, May 17 2020

Status

approved