A041114 Numerators of continued fraction convergents to sqrt(66).

8, 65, 1048, 8449, 136232, 1098305, 17709112, 142771201, 2302048328, 18559157825, 299248573528, 2412547746049, 38900012510312, 313612647828545, 5056702377767032, 40767231669964801, 657332409097203848, 5299426504447595585

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,frac,easy

Author

N. J. A. Sloane

Status

approved