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A055522
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Largest area of a Pythagorean triangle with n as length of one of the three sides (in fact as a leg).
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8
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6, 6, 30, 24, 84, 60, 180, 120, 330, 210, 546, 336, 840, 504, 1224, 720, 1710, 990, 2310, 1320, 3036, 1716, 3900, 2184, 4914, 2730, 6090, 3360, 7440, 4080, 8976, 4896, 10710, 5814, 12654, 6840, 14820, 7980, 17220, 9240, 19866, 10626, 22770, 12144, 25944
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OFFSET
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3,1
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LINKS
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Table of n, a(n) for n=3..47.
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FORMULA
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a(n) = n*A055523(n)/2.
a(2k) = k*(k+1)*(k-1), a(2k+1) = k*(k+1)*(2k+1).
O.g.f.: 6*x^3*(x+1+x^2)/((1-x)^4*(1+x)^4). a(2k+1)=A055112(k). a(2k)=A007531(k+1). [R. J. Mathar, Aug 06 2008]
a(n) = n*(3*(n^2-2)-(n^2+2)*(-1)^n)/16. - Luce ETIENNE, Jul 17 2015
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MAPLE
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seq(piecewise(n mod 2 = 0, n*(n^2-4)/8, n*(n^2-1)/4), n=3..60); # C. Ronaldo
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MATHEMATICA
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Table[n*(3*(n^2 - 2) - (n^2 + 2)*(-1)^n)/16, {n, 3, 50}] (* Wesley Ivan Hurt, Apr 27 2017 *)
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CROSSREFS
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Cf. A009112, A046079, A046080, A046081, A054435, A054436, A055523, A055524, A055525, A055526, A055527.
Sequence in context: A255462 A066714 A054436 * A078637 A147799 A071021
Adjacent sequences: A055519 A055520 A055521 * A055523 A055524 A055525
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KEYWORD
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nonn,easy
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AUTHOR
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Henry Bottomley, May 22 2000
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STATUS
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approved
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