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

1,2

Links

Table of n, a(n) for n=1..15.

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

Formula

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

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)) [From 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

Mathematica

Block[{a, nmax = 25}, 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]]] [From Terentyev Oleg, Nov 15 2009]
LinearRecurrence[{208, -2718, 208, -1}, {0, 12, 1848, 351780}, 20] (* Harvey P. Dale, Mar 02 2018 *)

Crossrefs

Cf. A103974.

Sequence in context: A049406 A049405 A229752 * A261946 A015028 A167745

Adjacent sequences: A104006 A104007 A104008 * A104010 A104011 A104012

Keyword

nonn,easy

Author

Zak Seidov, Feb 24 2005

Extensions

More terms from Rick L. Shepherd, Sep 05 2005

More terms from Colin Barker, Apr 10 2013

Status

approved