A073120 Areas of Pythagorean (or right) triangles with integer sides of the form (2mn, m^2 - n^2, m^2 + n^2).

6, 24, 30, 60, 84, 96, 120, 180, 210, 240, 330, 336, 384, 480, 486, 504, 546, 630, 720, 840, 924, 960, 990, 1224, 1320, 1344, 1386, 1536, 1560, 1710, 1716, 1920, 1944, 2016, 2184, 2310, 2340, 2430, 2520, 2574, 2730, 2880, 3036, 3360, 3570, 3696, 3750, 3840

Offset

1,1

Comments

Equivalently, integers of the form m*n*(m^2 - n^2) where m,n are positive integers with m > n. - James R. Buddenhagen, Aug 10 2008

The sequence giving the areas of all Pythagorean triangles is A009112 (sometimes called "Pythagorean numbers").

For example, the sequence does not contain 54, the area of the Pythagorean triangle with sides (9,12,15). - Robert Israel, Apr 03 2015

See also Theorem 2 of Mohanty and Mohanty. - T. D. Noe, Sep 24 2013

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Supriya Mohanty and S. P. Mohanty, Pythagorean Numbers, Fibonacci Quarterly 28 (1990), 31-42.

Eric Weisstein's World of Mathematics, Pythagorean Triple.

Konstantine Hermes Zelator, A little noticed right triangle, arXiv:0804.1340 [math.GM], 2008.

Formula

a(n) = A057102(n) / 4. - Max Alekseyev, Nov 14 2008

Example

6 = 3*4/2 is the area of the right triangle with sides 3 and 4.
84 = 7*24/2 is the area of the right triangle with sides 7 and 24.

Mathematica

nn = 16; t = Union[Flatten[Table[m*n*(m^2 - n^2), {m, 2, nn}, {n, m - 1}]]]; Select[t, # < nn*(nn^2 - 1) &]

Crossrefs

Cf. A009112, A002144, A003273, A046081, A057102, A024365.

Sequence in context: A332962 A350564 A132398 * A147778 A348714 A209452

Adjacent sequences: A073117 A073118 A073119 * A073121 A073122 A073123

Keyword

easy,nonn

Author

Zak Seidov, Aug 25 2002

Extensions

Description corrected by James R. Buddenhagen, Aug 10 2008, and by Max Alekseyev, Nov 12 2008

Edited by N. J. A. Sloane, Apr 06 2015

Status

approved