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Search: id:A073120
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| A073120 |
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Areas of right triangles with integer sides. |
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+0
5
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| 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)
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OFFSET
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1,1
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COMMENT
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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
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LINKS
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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].
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FORMULA
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a(n) = A057102(n) / 4 [From Max Alekseyev (maxale(AT)gmail.com), Nov 14 2008]
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EXAMPLE
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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.
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MATHEMATICA
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Union[Flatten[Table[m n (m^2-n^2), {m, 2, 50}, {n, 1, m-1}]]]
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CROSSREFS
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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
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KEYWORD
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easy,nonn
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AUTHOR
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Zak Seidov (zakseidov(AT)yahoo.com), Aug 25 2002
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EXTENSIONS
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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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