A042358 Numerators of continued fraction convergents to sqrt(706).

26, 27, 53, 186, 4889, 14853, 19742, 34595, 1818682, 1853277, 3671959, 12869154, 338269963, 1027679043, 1365949006, 2393628049, 125834607554, 128228235603, 254062843157, 890416765074, 23404898735081

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, 69190, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: (26 +27*x +53*x^2 +186*x^3 +4889*x^4 +14853*x^5 +19742*x^6 +34595*x^7 +19742*x^8 -14853*x^9 +4889*x^10 -186*x^11 +53*x^12 -27*x^13 +26*x^14 -x^15)/(1 -69190*x^8 +x^16). - Vincenzo Librandi, Nov 22 2013

a(n) = 69190*a(n-8) - a(n-16). - Vincenzo Librandi, Nov 22 2013

Mathematica

Numerator[Convergents[Sqrt[706], 30]] (* or *) CoefficientList[Series[(26 + 27 x + 53 x^2 + 186 x^3 + 4889 x^4 + 14853 x^5 + 19742 x^6 + 34595 x^7 + 19742 x^8 - 14853 x^9 + 4889 x^10 - 186 x^11 + 53 x^12 - 27 x^13 + 26 x^14 - x^15)/(1 - 69190 x^8 + x^16), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 22 2013 *)

Prog

(Magma) I:=[26, 27, 53, 186, 4889, 14853, 19742, 34595, 1818682, 1853277, 3671959, 12869154, 338269963, 1027679043, 1365949006, 2393628049]; [n le 16 select I[n] else 69190*Self(n-8)-Self(n-16): n in [1..30]]; // Vincenzo Librandi, Nov 22 2013

Crossrefs

Cf. A042359.

Sequence in context: A042366 A042368 A042360 * A042356 A042354 A042352

Adjacent sequences: A042355 A042356 A042357 * A042359 A042360 A042361

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved