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A041114
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Numerators of continued fraction convergents to sqrt(66).
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2
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8, 65, 1048, 8449, 136232, 1098305, 17709112, 142771201, 2302048328, 18559157825, 299248573528, 2412547746049, 38900012510312, 313612647828545, 5056702377767032, 40767231669964801, 657332409097203848, 5299426504447595585
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OFFSET
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0,1
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LINKS
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Nathaniel Johnston, Table of n, a(n) for n = 0..250
Index entries for linear recurrences with constant coefficients, signature (0,130,0,-1).
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FORMULA
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a(n) = 16*a(n-1) + a(n-2) for n>=2 even and a(n) = 8*a(n-1) + a(n-2) for n >= 2 odd. - Nathaniel Johnston, Jun 26 2011
From Colin Barker, Feb 28 2013: (Start)
a(n) = 130*a(n-2) - a(n-4).
G.f.: -(x^3-8*x^2-65*x-8) / (x^4-130*x^2+1). (End)
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MAPLE
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a := proc(n) option remember: if(n<=1)then return n+8^(n+1): fi: if(n mod 2 = 0)then return 16*a(n-1) + a(n-2): else return 8*a(n-1) + a(n-2): fi: end: seq(a(n), n=0..17); # Nathaniel Johnston, Jun 26 2011
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MATHEMATICA
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Numerator[Convergents[Sqrt[66], 30]] (* or *) LinearRecurrence[{0, 130, 0, -1}, {8, 65, 1048, 8449}, 30] (* Harvey P. Dale, Jan 31 2023 *)
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CROSSREFS
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Cf. A041115.
Sequence in context: A189431 A024105 A302316 * A360847 A320990 A015496
Adjacent sequences: A041111 A041112 A041113 * A041115 A041116 A041117
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KEYWORD
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nonn,cofr,easy
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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