A041291 Denominators of continued fraction convergents to sqrt(158).

1, 1, 2, 7, 86, 265, 351, 616, 15135, 15751, 30886, 108409, 1331794, 4103791, 5435585, 9539376, 234380609, 243919985, 478300594, 1678821767, 20624161798, 63551307161, 84175468959, 147726776120, 3629618095839, 3777344871959, 7406962967798, 25998233775353

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,15486,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^14 -x^13 +2*x^12 -7*x^11 +86*x^10 -265*x^9 +351*x^8 -616*x^7 -351*x^6 -265*x^5 -86*x^4 -7*x^3 -2*x^2 -x -1) / (x^16 -15486*x^8 +1). - Colin Barker, Nov 14 2013

a(n) = 15486*a(n-8) - a(n-16). - Vincenzo Librandi, Dec 14 2013

Mathematica

Denominator[Convergents[Sqrt[158], 30]] (* Harvey P. Dale, Aug 17 2013 *)
CoefficientList[Series[-(x^14 - x^13 + 2 x^12 - 7 x^11 + 86 x^10 - 265 x^9 + 351 x^8 - 616 x^7 - 351 x^6 - 265 x^5 - 86 x^4 - 7 x^3 - 2 x^2 - x - 1)/(x^16 - 15486 x^8 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 14 2013*)

Prog

(Magma) I:=[1, 1, 2, 7, 86, 265, 351, 616, 15135, 15751, 30886, 108409, 1331794, 4103791, 5435585, 9539376]; [n le 16 select I[n] else 15486*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 14 2013

Crossrefs

Cf. A041290, A010207.

Sequence in context: A062764 A163855 A268299 * A209331 A054919 A119157

Adjacent sequences: A041288 A041289 A041290 * A041292 A041293 A041294

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 14 2013

Status

approved