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Search: id:A158536
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| 11, 132, 495, 1100, 1947, 3036, 4367, 5940, 7755, 9812, 12111, 14652, 17435, 20460, 23727, 27236, 30987, 34980, 39215, 43692, 48411, 53372, 58575, 64020, 69707, 75636, 81807, 88220, 94875, 101772, 108911, 116292, 123915, 131780, 139887
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OFFSET
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0,1
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COMMENT
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From the Pell-type identity (22*n^2+1)^2 - (121*n^2+11) * (2*n)^2 = 1 we derive
(A158537(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.: 11*(1+9*x+12*x^2)/(1-x)^3.
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CROSSREFS
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Cf. A005843, A158537
Sequence in context: A068645 A097258 A044041 this_sequence A105280 A051431 A014994
Adjacent sequences: A158533 A158534 A158535 this_sequence A158537 A158538 A158539
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KEYWORD
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nonn,less,easy
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AUTHOR
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Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 21 2009
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EXTENSIONS
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Comment rewritten, a(0) added - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 16 2009
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