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A144536 Denominators of continued fraction convergents to sqrt(3)/2. 4
1, 1, 7, 15, 97, 209, 1351, 2911, 18817, 40545, 262087, 564719, 3650401, 7865521, 50843527, 109552575, 708158977, 1525870529, 9863382151, 21252634831, 137379191137, 296011017105, 1913445293767, 4122901604639, 26650854921601, 57424611447841, 371198523608647 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0, 14, 0, -1).

FORMULA

Empirical G.f.: (1+x-7*x^2+x^3)/(1-14*x^2+x^4). [Colin Barker, Jan 01 2012]

a(n) = 14*a(n-2) - a(n-4). - Sergei N. Gladkovskii, Jun 07 2015

a(n) = ((3+sqrt(3))*((-2+sqrt(3))^n + (2+sqrt(3))^n) - (-3+sqrt(3))*((-2-sqrt(3))^n + (2-sqrt(3))^n))/12. - Vaclav Kotesovec, Jun 08 2015

EXAMPLE

0, 1, 6/7, 13/15, 84/97, 181/209, 1170/1351, 2521/2911, 16296/18817, 35113/40545, ...

MAPLE

with(numtheory); Digits:=200: cf:=convert(evalf(sqrt(3)/2, confrac); [seq(nthconver(cf, i), i=0..100)];

MATHEMATICA

Denominator[Convergents [Sqrt[3]/2, 30]] (* Vincenzo Librandi, Feb 01 2014 *)

LinearRecurrence[{0, 14, 0, -1}, {1, 1, 7, 15}, 30] (* Harvey P. Dale, Sep 15 2017 *)

CROSSREFS

Cf. A126664, A144535, A002531/A002530.

Bisections give A011943, A028230.

Sequence in context: A177128 A177177 A041413 * A231399 A231466 A032004

Adjacent sequences:  A144533 A144534 A144535 * A144537 A144538 A144539

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane, Dec 29 2008

STATUS

approved

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Last modified June 20 00:47 EDT 2019. Contains 324223 sequences. (Running on oeis4.)