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

1,1

Links

Table of n, a(n) for n=1..42.

Wikipedia, Integer Triangle

Wikipedia, Pythagorean Triple.

Index entries related to Pythagorean Triples.

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

Example

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.

Crossrefs

Cf. A010814.

Sequence in context: A031692 A173141 A115592 * A273293 A097371 A179755

Adjacent sequences: A334805 A334806 A334807 * A334809 A334810 A334811

Keyword

nonn

Author

Wesley Ivan Hurt, May 12 2020

Status

approved