A041673 Denominators of continued fraction convergents to sqrt(355).

1, 1, 6, 19, 63, 82, 555, 637, 2466, 8035, 42641, 50676, 1866977, 1917653, 11455242, 36283379, 120305379, 156588758, 1059837927, 1216426685, 4709117982, 15343780631, 81428021137, 96771801768, 3565212884785, 3661984686553, 21875136317550, 69287393639203

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,1909618,0,0,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^22 -x^21 +6*x^20 -19*x^19 +63*x^18 -82*x^17 +555*x^16 -637*x^15 +2466*x^14 -8035*x^13 +42641*x^12 -50676*x^11 -42641*x^10 -8035*x^9 -2466*x^8 -637*x^7 -555*x^6 -82*x^5 -63*x^4 -19*x^3 -6*x^2 -x -1)/(x^24 -1909618*x^12 +1). - Vincenzo Librandi, Dec 22 2013

a(n) = 1909618*a(n-12) - a(n-24) for n>23. - Vincenzo Librandi, Dec 22 2013

Mathematica

Denominator/@Convergents[Sqrt[355], 40] (* Harvey P. Dale, May 11 2011 *)
CoefficientList[Series[-(x^22 - x^21 + 6 x^20 - 19 x^19 + 63 x^18 - 82 x^17 + 555 x^16 - 637 x^15 + 2466 x^14 - 8035 x^13 + 42641 x^12 - 50676 x^11 - 42641 x^10 - 8035 x^9 - 2466 x^8 - 637 x^7 - 555 x^6 - 82 x^5 - 63 x^4 - 19 x^3 - 6 x^2 - x - 1)/(x^24 - 1909618 x^12 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 22 2013 *)

Crossrefs

Cf. A041672 (numerators).

Sequence in context: A080926 A184189 A152098 * A137195 A055916 A266472

Adjacent sequences: A041670 A041671 A041672 * A041674 A041675 A041676

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Harvey P. Dale, May 11 2011

Status

approved