A042368 Numerators of continued fraction convergents to sqrt(711).

26, 27, 53, 80, 4213, 4293, 8506, 12799, 674054, 686853, 1360907, 2047760, 107844427, 109892187, 217736614, 327628801, 17254434266, 17582063067, 34836497333, 52418560400, 2760601638133, 2813020198533

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, 160, 0, 0, 0, -1).

Formula

G.f.: (26 +27*x +53*x^2 +80*x^3 +53*x^4 -27*x^5 +26*x^6 -x^7)/(1 -160*x^4 +x^8). - Vincenzo Librandi, Nov 22 2013

a(n) = 160*a(n-4) - a(n-8). - Vincenzo Librandi, Nov 22 2013

Mathematica

Numerator[Convergents[Sqrt[711], 30]] (* or *) CoefficientList[Series[(26 + 27 x + 53 x^2 + 80 x^3 + 53 x^4 - 27 x^5 + 26 x^6 - x^7)/(1 - 160 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 22 2013 *)

Prog

(Magma) I:=[26, 27, 53, 80, 4213, 4293, 8506, 12799]; [n le 8 select I[n] else 160*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 22 2013

Crossrefs

Cf. A042369.

Sequence in context: A042362 A042364 A042366 * A042360 A042358 A042356

Adjacent sequences: A042365 A042366 A042367 * A042369 A042370 A042371

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved