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 A041114 Numerators of continued fraction convergents to sqrt(66). 2
 8, 65, 1048, 8449, 136232, 1098305, 17709112, 142771201, 2302048328, 18559157825, 299248573528, 2412547746049, 38900012510312, 313612647828545, 5056702377767032, 40767231669964801, 657332409097203848, 5299426504447595585 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Nathaniel Johnston, Table of n, a(n) for n = 0..250 Index entries for linear recurrences with constant coefficients, signature (0,130,0,-1). FORMULA 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) MAPLE 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 MATHEMATICA Numerator[Convergents[Sqrt[66], 30]] (* or *) LinearRecurrence[{0, 130, 0, -1}, {8, 65, 1048, 8449}, 30] (* Harvey P. Dale, Jan 31 2023 *) CROSSREFS Cf. A041115. Sequence in context: A189431 A024105 A302316 * A360847 A320990 A015496 Adjacent sequences: A041111 A041112 A041113 * A041115 A041116 A041117 KEYWORD nonn,cofr,easy AUTHOR STATUS approved

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Last modified March 25 07:42 EDT 2023. Contains 361511 sequences. (Running on oeis4.)