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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 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

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