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A042314 Numerators of continued fraction convergents to sqrt(684). 2
26, 157, 183, 340, 4263, 4603, 8866, 57799, 3014414, 18144283, 21158697, 39302980, 492794457, 532097437, 1024891894, 6681448801, 348460229546, 2097442826077, 2445903055623, 4543345881700, 56966053636023 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,115598,0,0,0,0,0,0,0,-1).

FORMULA

G.f.: -(x^15 -26*x^14 +157*x^13 -183*x^12 +340*x^11 -4263*x^10 +4603*x^9 -8866*x^8 -57799*x^7 -8866*x^6 -4603*x^5 -4263*x^4 -340*x^3 -183*x^2 -157*x -26)/(x^16 -115598*x^8 +1). - Vincenzo Librandi Nov 21 2013

a(n) = 115598*a(n-8) - a(n-16), - Vincenzo Librandi, Nov 21 2013

MATHEMATICA

Numerator[Convergents[Sqrt[684], 30]] (* or *) CoefficientList[Series[-(x^15 - 26 x^14 + 157 x^13 - 183 x^12 + 340 x^11 - 4263 x^10 + 4603 x^9 - 8866 x^8 - 57799 x^7 - 8866 x^6 - 4603 x^5 - 4263 x^4 - 340 x^3 - 183 x^2 - 157 x - 26)/(x^16 - 115598 x^8 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 21 2013 *)

PROG

(Magma) I:=[26, 157, 183, 340, 4263, 4603, 8866, 57799, 3014414, 18144283, 21158697, 39302980, 492794457, 532097437, 1024891894, 6681448801]; [n le 16 select I[n] else 115598*Self(n-8)-Self(n-16): n in [1..30]]; // Vincenzo Librandi, Nov 21 2013

CROSSREFS

Cf. A042315.

Sequence in context: A192289 A230906 A232585 * A280213 A200874 A027280

Adjacent sequences:  A042311 A042312 A042313 * A042315 A042316 A042317

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified September 24 23:43 EDT 2022. Contains 356951 sequences. (Running on oeis4.)