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%I #19 Apr 27 2017 22:49:28
%S 6,6,30,24,84,60,180,120,330,210,546,336,840,504,1224,720,1710,990,
%T 2310,1320,3036,1716,3900,2184,4914,2730,6090,3360,7440,4080,8976,
%U 4896,10710,5814,12654,6840,14820,7980,17220,9240,19866,10626,22770,12144,25944
%N Largest area of a Pythagorean triangle with n as length of one of the three sides (in fact as a leg).
%F a(n) = n*A055523(n)/2.
%F a(2k) = k*(k+1)*(k-1), a(2k+1) = k*(k+1)*(2k+1).
%F 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]
%F a(n) = n*(3*(n^2-2)-(n^2+2)*(-1)^n)/16. - _Luce ETIENNE_, Jul 17 2015
%p seq(piecewise(n mod 2 = 0,n*(n^2-4)/8,n*(n^2-1)/4),n=3..60); # C. Ronaldo
%t Table[n*(3*(n^2 - 2) - (n^2 + 2)*(-1)^n)/16, {n, 3, 50}] (* _Wesley Ivan Hurt_, Apr 27 2017 *)
%Y Cf. A009112, A046079, A046080, A046081, A054435, A054436, A055523, A055524, A055525, A055526, A055527.
%K nonn,easy
%O 3,1
%A _Henry Bottomley_, May 22 2000
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