A096382 Consider a Pythagorean triangle with sides a=u^2-v^2, b=2uv, c=u^2+v^2. The sequence is the area of the triangle when v=2, u=3,4,5,...

30, 96, 210, 384, 630, 960, 1386, 1920, 2574, 3360, 4290, 5376, 6630, 8064, 9690, 11520, 13566, 15840, 18354, 21120, 24150, 27456, 31050, 34944, 39150, 43680, 48546, 53760, 59334, 65280, 71610, 78336, 85470, 93024, 101010, 109440, 118326, 127680, 137514

Offset

3,1

Links

Table of n, a(n) for n=3..41.

Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1).

Formula

The area of a Pythagorean triangle of sides a < b < c is A = a*b/2. Substituting a=u^2-v^2, b=2uv into A and simplifying, we get A = uv(u^2-v^2).

a(n) = (n-2)*(n*2)*(n+2), n >= 3. - Zerinvary Lajos, Mar 05 2007

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(2)=30, a(3)=96, a(4)=210, a(5)=384. - Harvey P. Dale, May 06 2012

Maple

seq((n-2)*(n*2)*(n+2), n=3..39); # Zerinvary Lajos, Mar 05 2007

Mathematica

Table[2*n^3 + 6*n^2 - 2*n - 6, {n, 2, 60}] (* Vladimir Joseph Stephan Orlovsky, Jul 08 2011 *)
LinearRecurrence[{4, -6, 4, -1}, {30, 96, 210, 384}, 40] (* Harvey P. Dale, May 06 2012 *)

Prog

(PARI) areagen(n, u) = for(v=u+1, n, print1(u*v*(v^2-u^2)", "))

Crossrefs

Sequence in context: A033573 A035076 A308508 * A303859 A002758 A346855

Adjacent sequences: A096379 A096380 A096381 * A096383 A096384 A096385

Keyword

nonn,easy

Author

Cino Hilliard, Aug 05 2004

Extensions

Corrected by N. J. A. Sloane, Jan 28 2019 at the suggestion of Jon E. Schoenfield.

Status

approved