A104009 Area of (a,a,a+1)-integer triangle. Corresponding a's are in A103974.

0, 12, 1848, 351780, 68149872, 13219419708, 2564481115560, 497495864091732, 96511629630137568, 18722758603319903340, 3632118656731075949592, 704612296637707504759428, 136691153428925957468727120, 26517379152913151616036727452, 5144234864511696770165553009288

Offset: 1

Author

Zak Seidov, Feb 24 2005

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (208,-2718,208,-1).

Crossrefs

Cf. A103974.

Programs

Mathematica

Block[{a, nmax = 14}, a[n_] := ((-(2 - Sqrt[3])^(2 n) + (2 + Sqrt[3])^( 2 n)) (4 + (2 - Sqrt[3])^(2 n) + (2 + Sqrt[3])^(2 n)))/( 12 Sqrt[3]); Expand[a /@ Range[0, nmax]]] (* Terentyev Oleg, Nov 15 2009 *)
LinearRecurrence[{208,-2718,208,-1},{0,12,1848,351780},20] (* Harvey P. Dale, Mar 02 2018 *)

Formula

s(n) = ((a+1)/4)*sqrt((3*a+1)*(a-1)) where a=A103974(n).

a(n+1) = (((2 + sqrt(3))^(2*n) - (2 - sqrt(3))^(2*n))*(4 + (2 - sqrt(3))^(2*n) + (2 + sqrt(3))^(2*n)))/(12*sqrt(3)). - Terentyev Oleg, Nov 15 2009

G.f.: 12*x^2*(x^2-54*x+1) / ((x^2-194*x+1)*(x^2-14*x+1)). - Colin Barker, Apr 10 2013

Extensions

More terms from Rick L. Shepherd, Sep 05 2005

More terms from Colin Barker, Apr 10 2013