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Search: id:A158672
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| 30, 930, 3630, 8130, 14430, 22530, 32430, 44130, 57630, 72930, 90030, 108930, 129630, 152130, 176430, 202530, 230430, 260130, 291630, 324930, 360030, 396930, 435630, 476130, 518430, 562530, 608430, 656130, 705630, 756930, 810030, 864930, 921630
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OFFSET
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0,1
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COMMENT
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The identity (60*n^2+1)^2 - (900*n^2+30) * (2*n)^2 = 1 can be written as
the Pell equation (A158673(n))^2 - a(n) * (A005843(n))^2 = 1.
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LINKS
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Vincenzo Librandi, X^2-AY^2=1
Edward Everett Withford, Pell Equation
Wolfram MathWorld, Pell Equation
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FORMULA
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a(n)= 3*a(n-1) -3*a(n-2) +a(n-3). G.f.: -30*(1+28*x+31*x^2)/(x-1)^3.
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CROSSREFS
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Cf. A005843, A158673
Sequence in context: A042742 A144350 A111216 this_sequence A004994 A061466 A160313
Adjacent sequences: A158669 A158670 A158671 this_sequence A158673 A158674 A158675
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KEYWORD
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nonn,easy
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AUTHOR
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Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 24 2009
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EXTENSIONS
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Comment rewritten, a(0) added and formula replaced by R. J. Mathar, (mathar(AT)strw.leidenuniv.nl), Oct 22 2009
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