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A341929
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Bisection of the numerators of the convergents of cf (1,1,6,1,6,1,...,6,1).
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1
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1, 2, 15, 118, 929, 7314, 57583, 453350, 3569217, 28100386, 221233871, 1741770582, 13712930785, 107961675698, 849980474799, 6691882122694, 52685076506753, 414788729931330, 3265624762943887, 25710209373619766, 202416050226014241, 1593618192434494162, 12546529489249939055, 98778617721565018278
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OFFSET
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0,2
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COMMENTS
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15*a(n)^2 - 11 is a square for all terms.
x = a(n) and y = a(n+1) satisfy the equation x^2 + y^2 - 8*x*y = -11.
x = a(n) and y = a(n+2) satisfy x^2 + y^2 - 62*x*y = -704.
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LINKS
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FORMULA
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a(n) = 8*a(n-1) - a(n-2) for n >= 2.
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EXAMPLE
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a(3) = 8*15 - 2 = 118.
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MATHEMATICA
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LinearRecurrence [{8, -1}, {1, 2}, 15]
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PROG
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(PARI) my(p=Mod('x, 'x^2-8*'x+1)); a(n) = subst(lift(p^n), 'x, 2); \\ Kevin Ryde, Feb 27 2021
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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