A103975 Smaller side in (a,a+1,a+1)-integer triangle with integer area.

16, 240, 3360, 46816, 652080, 9082320, 126500416, 1761923520, 24540428880, 341804080816, 4760716702560, 66308229755040, 923554499868016, 12863454768397200, 179164812257692800, 2495443916839302016, 34757050023492535440, 484103256412056194160

Offset: 1

Author

Zak Seidov, Feb 23 2005

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (15,-15,1).

Crossrefs

Cf. A102341, A103974, A016064, A011945, A103772.

Corresponding areas are given by A104008.

Programs

Mathematica

a[n_] := 1/3 (-4 + (2 - Sqrt[3])^(1 + 2 n) + (2 + Sqrt[3])^(1 + 2 n)); A103975 = Expand[a /@ Range[1, 25]] (* Terentyev Oleg, Nov 12 2009 *)
LinearRecurrence[{15,-15,1},{16,240,3360},30] (* Harvey P. Dale, Apr 25 2012 *)

Formula

a(n) = 15*a(n-1) - 15*a(n-2) + a(n-3) - Max Alekseyev, May 31 2007

a(n) = 2*A120892(2*n+1) - Max Alekseyev, May 31 2007

a(n) = (1/3)*((2 - sqrt(3))^(1 + 2*n) + (2 + sqrt(3))^(1 + 2*n) - 4). [Terentyev Oleg, Nov 12 2009]

a(n) = (4/3)*(A001570(n+1)-1).

G.f.: -16*x / ((x-1)*(x^2-14*x+1)). - Colin Barker, Apr 09 2013

Extensions

More terms from Robert G. Wilson v, Mar 24 2005

More terms from Colin Barker, Apr 09 2013