A041341 Denominators of continued fraction convergents to sqrt(184).

1, 1, 2, 7, 16, 23, 62, 85, 232, 781, 1013, 1794, 47657, 49451, 97108, 340775, 778658, 1119433, 3017524, 4136957, 11291438, 38011271, 49302709, 87313980, 2319466189, 2406780169, 4726246358, 16585519243, 37897284844, 54482804087, 146862893018, 201345697105

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, 48670, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^22 -x^21 +2*x^20 -7*x^19 +16*x^18 -23*x^17 +62*x^16 -85*x^15 +232*x^14 -781*x^13 +1013*x^12 -1794*x^11 -1013*x^10 -781*x^9 -232*x^8 -85*x^7 -62*x^6 -23*x^5 -16*x^4 -7*x^3 -2*x^2 -x -1) / (x^24 -48670*x^12 +1). - Colin Barker, Nov 15 2013

a(n) = 48670*a(n-12) - a(n-24). - Vincenzo Librandi, Dec 16 2013

Mathematica

Denominator[Convergents[Sqrt[184], 30]] (* Vincenzo Librandi, Dec 16 2013 *)

Prog

(Magma) I:=[1, 1, 2, 7, 16, 23, 62, 85, 232, 781, 1013, 1794, 47657, 49451, 97108, 340775, 778658, 1119433, 3017524, 4136957, 11291438, 38011271, 49302709, 87313980]; [n le 24 select I[n] else 48670*Self(n-12)-Self(n-24): n in [1..40]]; // Vincenzo Librandi, Dec 16 2013

Crossrefs

Cf. A041340, A010226.

Sequence in context: A167236 A041573 A211053 * A296857 A229595 A083508

Adjacent sequences: A041338 A041339 A041340 * A041342 A041343 A041344

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 15 2013

Status

approved