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

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy
• less

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).

Crossrefs

Cf. A041841.

Programs

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 *)

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]