A041823 Denominators of continued fraction convergents to sqrt(432).

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

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