A253803 a(n) gives one fourth of the even leg of one of the two Pythagorean triangles with hypotenuse A080109(n) = A002144(n)^2. The odd leg is given in A253802(n).

6, 39, 60, 210, 210, 410, 630, 915, 1320, 1780, 2340, 990, 2730, 3164, 4620, 5215, 5610, 4290, 8145, 8106, 2730, 6630, 12116, 12540, 4080, 17485, 17451, 18480, 9690, 24414

Offset

1,1

Comments

See A253802 for comments and the Dickson reference.

References

L. E. Dickson, History of the Theory of Numbers, Carnegie Institution, Publ. No. 256, Vol. II, Washington D.C., 1920, p. 227.

Links

Table of n, a(n) for n=1..30.

Formula

a(n) = sqrt(A080109(n)^2 - A253802(n)^2)/4, n >= 1.

Example

n = 7: A080175(7) = 7890481 = 53^4 = 2809^2; A002144(7)^4 = A253802(7)^2 + (4*a(7))^2 = 1241^2 + (4*630)^2.
The other Pythagorean triangle with hypotenuse
53^2 = 2809 has odd leg A253804(7) = 2385 and even leg 4*A253305(7) = 4*371 = 1484: 53^4 = 2385^2 + (4*371)^2.

Crossrefs

Cf. A002144, A080109, A253802, A253804, A253805.

Sequence in context: A366212 A061423 A080298 * A355412 A058897 A058985

Adjacent sequences: A253800 A253801 A253802 * A253804 A253805 A253806

Keyword

nonn,easy

Author

Wolfdieter Lang, Jan 14 2015

Status

approved