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A132596
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Sequence allows us to find X values of the equation: X(X + 1) - 6*Y^2 = 0.
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3
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0, 2, 24, 242, 2400, 23762, 235224, 2328482, 23049600, 228167522, 2258625624, 22358088722, 221322261600, 2190864527282, 21687323011224, 214682365584962, 2125136332838400, 21036680962799042, 208241673295152024
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Or, 3*A000217(X) is a square. [From Zak Seidov (zakseidov(AT)yahoo.com), Apr 08 2009]
"You can find an infinite number of [different] triangular numbers such that when multipled together form a square number. For example, for every triangular number, T_n, there are an infinite number of other triangular numbers, T_m, such that T_n*T_m is a square. For example, T_2 * T_24 = 30^2." Pickover. [From Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 01 2010]
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REFERENCES
| Clifford A. Pickover, The Loom of God, Tapestries of Mathematics and Mysticism, Sterling, NY, 2009, page 33. [From Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 01 2010]
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (11,-11,1). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 20 2010]
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FORMULA
| a(0)=0, a(1)=2 and a(n)=10*a(n-1) - a(n-2) + 4.
a(n)=-1/2+(1/4)*[5+2*sqrt(6)]^n+(1/4)*[5-2*sqrt(6)]^n, with n>=0 - Paolo P. Lava (paoloplava(AT)gmail.com), Jul 15 2008
a(n) = (A001079(n) - 1)/2 [From Max Alekseyev (maxale(AT)gmail.com), Nov 13 2009]
a(n) = +11*a(n-1) -11*a(n-2) +a(n-3) = 2*A098297(n). G.f.: -2*x*(1+x) / ( (x-1)*(x^2-10*x+1) ). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 20 2010]
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CROSSREFS
| Cf. A007654.
Sequence in context: A180388 A025131 A143407 * A099669 A019520 A187584
Adjacent sequences: A132593 A132594 A132595 * A132597 A132598 A132599
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KEYWORD
| nonn
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AUTHOR
| Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Nov 14 2007
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