A041205 Denominators of continued fraction convergents to sqrt(113).

1, 1, 2, 3, 8, 19, 27, 46, 73, 1506, 1579, 3085, 4664, 12413, 29490, 41903, 71393, 113296, 2337313, 2450609, 4787922, 7238531, 19264984, 45768499, 65033483, 110801982, 175835465, 3627511282, 3803346747, 7430858029, 11234204776, 29899267581, 71032739938

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,1552,0,0,0,0,0,0,0,0,1).

Formula

G.f.: -(x^16 -x^15 +2*x^14 -3*x^13 +8*x^12 -19*x^11 +27*x^10 -46*x^9 +73*x^8 +46*x^7 +27*x^6 +19*x^5 +8*x^4 +3*x^3 +2*x^2 +x +1) / (x^18 +1552*x^9 -1). - Colin Barker, Nov 14 2013

a(n) = 1552*a(n-9) + a(n-18). - Vincenzo Librandi, Dec 13 2013

Mathematica

Denominator[Convergents[Sqrt[113], 40]] (* Harvey P. Dale, Feb 05 2012 *)
CoefficientList[Series[-(x^16 - x^15 + 2 x^14 - 3 x^13 + 8 x^12 - 19 x^11 + 27 x^10 - 46 x^9 + 73 x^8 + 46 x^7 + 27 x^6 + 19 x^5 + 8 x^4 + 3 x^3 + 2 x^2 + x + 1)/(x^18 + 1552 x^9 - 1), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 13 2013 *)

Prog

(Magma) I:=[1, 1, 2, 3, 8, 19, 27, 46, 73, 1506, 1579, 3085, 4664, 12413, 29490, 41903, 71393, 113296]; [n le 18 select I[n] else 1552*Self(n-9)+Self(n-18): n in [1..40]]; // Vincenzo Librandi, Dec 13 2013

Crossrefs

Cf. A041204, A010178.

Sequence in context: A240645 A273754 A242099 * A002356 A166302 A347736

Adjacent sequences: A041202 A041203 A041204 * A041206 A041207 A041208

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 14 2013

Status

approved