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A041823 Denominators of continued fraction convergents to sqrt(432). 2
1, 1, 4, 5, 9, 14, 51, 65, 2651, 2716, 10799, 13515, 24314, 37829, 137801, 175630, 7163001, 7338631, 29178894, 36517525, 65696419, 102213944, 372338251, 474552195, 19354426051, 19828978246, 78841360789, 98670339035, 177511699824, 276182038859, 1006057816401 (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 (0,0,0,0,0,0,0,2702,0,0,0,0,0,0,0,-1).

FORMULA

G.f.: -(x^2-x-1)*(x^4+5*x^2+1)*(x^8+13*x^4+1) / ((x^8-52*x^4+1)*(x^8+52*x^4+1)). - Colin Barker, Nov 25 2013

a(n) = 2702*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Dec 25 2013

MATHEMATICA

Denominator[Convergents[Sqrt[432], 30]] (* Vincenzo Librandi, Dec 25 2013 *)

PROG

(Magma) I:=[1, 1, 4, 5, 9, 14, 51, 65, 2651, 2716, 10799, 13515, 24314, 37829, 137801, 175630]; [n le 16 select I[n] else 2702*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 25 2013

CROSSREFS

Cf. A041822, A040411.

Sequence in context: A042765 A041353 A121052 * A042489 A217685 A251632

Adjacent sequences: A041820 A041821 A041822 * A041824 A041825 A041826

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Colin Barker, Nov 25 2013

STATUS

approved

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Last modified February 6 01:28 EST 2023. Contains 360091 sequences. (Running on oeis4.)