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A041043 Denominators of continued fraction convergents to sqrt(27). 3
1, 5, 51, 260, 2651, 13515, 137801, 702520, 7163001, 36517525, 372338251, 1898208780, 19354426051, 98670339035, 1006057816401, 5128959421040, 52295652026801, 266607219555045, 2718367847577251, 13858446457441300 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,52,0,-1).

FORMULA

a(n) = 52*a(n-2)-a(n-4). G.f.: -(x^2-5*x-1)/(x^4-52*x^2+1). - Colin Barker, Jul 15 2012

From Gerry Martens, Jul 11 2015: (Start)

Interspersion of 2 sequences [a0(n),a1(n)]:

a0(n) = ((9+5*sqrt(3))/(26+15*sqrt(3))^n+(9-5*sqrt(3))*(26+15*sqrt(3))^n)/18.

a1(n) = (-1/(26+15*sqrt(3))^n+(26+15*sqrt(3))^n)/(6*sqrt(3)). (End)

MATHEMATICA

Denominator[Convergents[Sqrt[27], 50]] (* Harvey P. Dale, Apr 22 2012 *)

CoefficientList[Series[- (x^2 - 5 x - 1)/(x^4 - 52 x^2 + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 22 2013 *)

a0[n_] := (9+5*Sqrt[3]+(9-5*Sqrt[3])*(26+15*Sqrt[3])^(2*n))/(18*(26+15*Sqrt[3])^n) // Simplify

a1[n_] := (-1+(26+15*Sqrt[3])^(2*n))/(6*Sqrt[3]*(26+15*Sqrt[3])^n) // FullSimplify

Flatten[MapIndexed[{a0[#], a1[#]}&, Range[10]]] (* Gerry Martens, Jul 10 2015 *)

CROSSREFS

Cf. A010482, A041042.

Sequence in context: A134938 A068540 A208997 * A145641 A317782 A195211

Adjacent sequences:  A041040 A041041 A041042 * A041044 A041045 A041046

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified January 24 04:35 EST 2020. Contains 331183 sequences. (Running on oeis4.)