A041075 Denominators of continued fraction convergents to sqrt(44).

1, 1, 2, 3, 8, 11, 19, 30, 379, 409, 788, 1197, 3182, 4379, 7561, 11940, 150841, 162781, 313622, 476403, 1266428, 1742831, 3009259, 4752090, 60034339, 64786429, 124820768, 189607197, 504035162, 693642359, 1197677521, 1891319880, 23893516081, 25784835961

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,398,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^2-x-1)*(x^4+3*x^2+1)*(x^8+10*x^4+1) / ((x^8-20*x^4+1)*(x^8+20*x^4+1)). - Colin Barker, Nov 12 2013

a(n) = 398*a(n-8) - a(n-16). - Vincenzo Librandi, Dec 11 2013

Mathematica

Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[44], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 22 2011 *)
Denominator[Convergents[Sqrt[44], 30]] (* Vincenzo Librandi, Dec 11 2013 *)

Prog

(Magma) I:=[1, 1, 2, 3, 8, 11, 19, 30, 379, 409, 788, 1197, 3182, 4379, 7561, 11940]; [n le 16 select I[n] else 398*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 11 2013

Crossrefs

Cf. A010498, A041074.

Sequence in context: A291202 A091076 A112595 * A041893 A206241 A295333

Adjacent sequences: A041072 A041073 A041074 * A041076 A041077 A041078

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 12 2013

Status

approved