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A042656 Numerators of continued fraction convergents to sqrt(858). 2
29, 88, 205, 703, 40979, 123640, 288259, 988417, 57616445, 173837752, 405291949, 1389713599, 81008680691, 244415755672, 569840192035, 1953936331777, 113898147435101, 343648378637080, 801194904709261 (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, 1406, 0, 0, 0, -1).

FORMULA

G.f.: (29 +88*x +205*x^2 +703*x^3 +205*x^4 -88*x^5 +29*x^6 -x^7)/(1 -1406*x^4 +x^8). - Vincenzo Librandi, Nov 30 2013

a(n) = 1406*a(n-4) - a(n-8). - Vincenzo Librandi, Nov 30 2013

MATHEMATICA

Numerator[Convergents[Sqrt[858], 30]] (* or *) CoefficientList[Series[(29 + 88 x + 205 x^2 + 703 x^3 + 205 x^4 - 88 x^5 + 29 x^6 - x^7)/(1 - 1406 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 30 2013 *)

LinearRecurrence[{0, 0, 0, 1406, 0, 0, 0, -1}, {29, 88, 205, 703, 40979, 123640, 288259, 988417}, 20] (* Harvey P. Dale, Mar 01 2019 *)

PROG

(MAGMA) I:=[29, 88, 205, 703, 40979, 123640, 288259, 988417]; [n le 8 select I[n] else 1406*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 30 2013

CROSSREFS

Cf. A042657.

Sequence in context: A032508 A042654 A042652 * A042658 A042660 A047650

Adjacent sequences:  A042653 A042654 A042655 * A042657 A042658 A042659

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified May 19 10:55 EDT 2019. Contains 323390 sequences. (Running on oeis4.)