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A042510 Numerators of continued fraction convergents to sqrt(783). 2
27, 28, 1539, 1567, 86157, 87724, 4823253, 4910977, 270016011, 274926988, 15116073363, 15391000351, 846230092317, 861621092668, 47373769096389, 48235390189057, 2652084839305467, 2700320229494524 (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 (0,56,0,-1).

FORMULA

G.f.: (27 + 28*x + 27*x^2 - x^3)/(1 - 56*x^2 + x^4). - Vincenzo Librandi, Nov 26 2013

a(n) = 56*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 26 2013

MATHEMATICA

Numerator[Convergents[Sqrt[783], 30]] (* or *) CoefficientList[Series[(27 + 28 x + 27 x^2 - x^3)/(1 - 56 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 25 2013 *)

LinearRecurrence[{0, 56, 0, -1}, {27, 28, 1539, 1567}, 30] (* Harvey P. Dale, Apr 28 2016 *)

PROG

(MAGMA) I:=[27, 28, 1539, 1567]; [n le 4 select I[n] else 56*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 26 2013

CROSSREFS

Cf. A042511.

Sequence in context: A041363 A042508 A042509 * A157251 A214832 A050876

Adjacent sequences:  A042507 A042508 A042509 * A042511 A042512 A042513

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified November 19 20:42 EST 2019. Contains 329323 sequences. (Running on oeis4.)