A334808 Consider all the Pythagorean triangles with perimeter A010814(n). Then a(n) is the sum of the areas of the squares on all of their sides.

50, 200, 338, 450, 578, 800, 1250, 2602, 1682, 1800, 2312, 5188, 6404, 3200, 4050, 5000, 15610, 5618, 13492, 6728, 15650, 8450, 8450, 8450, 9248, 32002, 10658, 36866, 14450, 12800, 14450, 14450, 14450, 15842, 31700, 16200, 20402, 20000, 18050, 18818, 87978, 69164

Offset: 1

Author

Wesley Ivan Hurt, May 12 2020

Keywords

• nonn

Examples

			a(1) = 50; there is one Pythagorean triangle with perimeter A010814(1) = 12, [3,4,5]. The sum of the areas of the squares on its sides is 3^2 + 4^2 + 5^2 = 9 + 16 + 25 = 50.
a(2) = 200; there is one Pythagorean triangle with perimeter A010814(2) = 24, [6,8,10]. The sum of the areas of the squares on its sides is 6^2 + 8^2 + 10^2 = 36 + 64 + 100 = 200.
		

Links

• Wikipedia, Integer Triangle
• Wikipedia, Pythagorean Triple.
• Index entries related to Pythagorean Triples.

Crossrefs

Cf. A010814.

Formula

a(n) = 2 * Sum_{k=1..floor(c(n)/3)} Sum_{i=k..floor((c(n)-k)/2)} sign(floor((i+k)/(c(n)-i-k+1))) * [i^2 + k^2 = (c(n)-i-k)^2] * (c(n)-i-k)^2, where c = A010814. - Wesley Ivan Hurt, May 13 2020