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

1,1

Links

Table of n, a(n) for n=1..18.

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

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

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 *)

Crossrefs

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

Corresponding areas are given by A104008.

Sequence in context: A283411 A161591 A227440 * A162791 A060198 A097829

Adjacent sequences: A103972 A103973 A103974 * A103976 A103977 A103978

Keyword

nonn,easy

Author

Zak Seidov, Feb 23 2005

Extensions

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

More terms from Colin Barker, Apr 09 2013

Status

approved