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%I #19 Jan 31 2023 14:57:20
%S 8,65,1048,8449,136232,1098305,17709112,142771201,2302048328,
%T 18559157825,299248573528,2412547746049,38900012510312,
%U 313612647828545,5056702377767032,40767231669964801,657332409097203848,5299426504447595585
%N Numerators of continued fraction convergents to sqrt(66).
%H Nathaniel Johnston, <a href="/A041114/b041114.txt">Table of n, a(n) for n = 0..250</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,130,0,-1).
%F 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
%F From _Colin Barker_, Feb 28 2013: (Start)
%F a(n) = 130*a(n-2) - a(n-4).
%F G.f.: -(x^3-8*x^2-65*x-8) / (x^4-130*x^2+1). (End)
%p 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
%t Numerator[Convergents[Sqrt[66],30]] (* or *) LinearRecurrence[{0,130,0,-1},{8,65,1048,8449},30] (* _Harvey P. Dale_, Jan 31 2023 *)
%Y Cf. A041115.
%K nonn,cofr,easy
%O 0,1
%A _N. J. A. Sloane_
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