A041840 Numerators of continued fraction convergents to sqrt(442).

21, 883, 37107, 1559377, 65530941, 2753858899, 115727604699, 4863313256257, 204374884367493, 8588608456690963, 360925930065387939, 15167477671202984401, 637394988120590732781, 26785756978736013761203

Offset

0,1

Links

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

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (42,1).

Formula

G.f.: (21+x)/(1-42*x-x^2). [Philippe Deléham, Nov 23 2008]

a(n) = 42*a(n-1)+a(n-2) for n>1, a(0)=21, a(1)=883. [Philippe Deléham, Nov 23 2008]

Mathematica

Numerator[Convergents[Sqrt[442], 30]] (* or *) LinearRecurrence[{42, 1}, {21, 883}, 30] (* Harvey P. Dale, Nov 20 2012 *)
CoefficientList[Series[(21 + x)/(1 - 42 x - x^2), {x, 0, 25}], x] (* Vincenzo Librandi, Nov 10 2013 *)

Crossrefs

Cf. A041841.

Sequence in context: A204196 A238653 A041843 * A012793 A015305 A101732

Adjacent sequences: A041837 A041838 A041839 * A041841 A041842 A041843

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved