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A104009 Area of (a,a,a+1)-integer triangle. Corresponding a's are in A103974. 1
0, 12, 1848, 351780, 68149872, 13219419708, 2564481115560, 497495864091732, 96511629630137568, 18722758603319903340, 3632118656731075949592, 704612296637707504759428, 136691153428925957468727120, 26517379152913151616036727452, 5144234864511696770165553009288 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
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
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

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Last modified April 20 09:04 EDT 2024. Contains 371799 sequences. (Running on oeis4.)