

A073120


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


10



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
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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), 3142.
Eric Weisstein's World of Mathematics, Pythagorean Triple.
Konstantine Hermes Zelator, A little noticed right triangle, arXiv: 0804.1340 [math.GM].


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: A334788 A332962 A132398 * A147778 A209452 A275302
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



