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A132594
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Sequence allows us to find X values of the equation: X(X + 1) - 7*Y^2 = 0.
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0
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0, 63, 16128, 4096575, 1040514048, 264286471743, 67127723308800, 17050177433963583, 4330677940503441408, 1099975146710440154175, 279389356586511295719168, 70963796597827158672514623
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| The full set of integer solutions to this equation consists of the pairs [X(i),Y(i)] = [1+-A001081(i), Y(i)=A001080(i)]. The present generates every second one of them: a(n) = [A001081(2n)-1]/2. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 20 2007
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FORMULA
| a(0)=0, a(1)=63 and a(n)=254*a(n-1) - a(n-2) + 126.
G.f.: -63*x*(1+x)/(-1+x)/(1-254*x+x^2). a(n) = [A001081(2n)-1]/2. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 20 2007
a(n)=-(1/2)+(1/4)*[127-48*sqrt(7)]^n+(1/4)*[127+48*sqrt(7)]^n, with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Sep 26 2008]
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CROSSREFS
| Cf. A007654.
Cf. A001080, A001081.
Sequence in context: A160871 A183525 A062208 * A177233 A183482 A001238
Adjacent sequences: A132591 A132592 A132593 * A132595 A132596 A132597
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KEYWORD
| nonn
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AUTHOR
| Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Nov 14 2007
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EXTENSIONS
| More terms from Max Alekseyev (maxale(AT)gmail.com), Nov 13 2009
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