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A073120 Areas of right triangles with integer sides. +0
5
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 (list; graph; listen)
OFFSET

1,1

COMMENT

Areas of Pythagorean right triangles of the form (2mn, m^2-n^2, m^2+n^2), or equivalently integers of the form m*n*(m^2-n^2) where m,n are positive integers with m>n. - James Buddenhagen (jbuddenh(AT)gmail.com), Aug 10 2008

LINKS

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

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

FORMULA

a(n) = A057102(n) / 4 [From Max Alekseyev (maxale(AT)gmail.com), 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

Union[Flatten[Table[m n (m^2-n^2), {m, 2, 50}, {n, 1, m-1}]]]

CROSSREFS

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

Sequence in context: A057101 A057228 A132398 this_sequence A147778 A128459 A147826

Adjacent sequences: A073117 A073118 A073119 this_sequence A073121 A073122 A073123

KEYWORD

easy,nonn

AUTHOR

Zak Seidov (zakseidov(AT)yahoo.com), Aug 25 2002

EXTENSIONS

Description corrected by James Buddenhagen (jbuddenh(AT)gmail.com), Aug 10 2008, and by Max Alekseyev (maxale(AT)gmail.com), Nov 12 2008

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Last modified November 29 12:46 EST 2009. Contains 167659 sequences.


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