A055522 Largest area of a Pythagorean triangle with n as length of one of the three sides (in fact as a leg).

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

Offset: 3

Author

Henry Bottomley, May 22 2000

Keywords

• nonn
• easy

Crossrefs

Cf. A009112, A046079, A046080, A046081, A054435, A054436, A055523, A055524, A055525, A055526, A055527.

Programs

Maple

seq(piecewise(n mod 2 = 0,n*(n^2-4)/8,n*(n^2-1)/4),n=3..60); # C. Ronaldo

Mathematica

Table[n*(3*(n^2 - 2) - (n^2 + 2)*(-1)^n)/16, {n, 3, 50}] (* Wesley Ivan Hurt, Apr 27 2017 *)

Formula

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