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A042624 Numerators of continued fraction convergents to sqrt(842). 2
29, 1683, 97643, 5664977, 328666309, 19068310899, 1106290698451, 64183928821057, 3723774162319757, 216043085343366963, 12534222724077603611, 727200961081844376401, 42190189965471051434869, 2447758218958402827598803 (list; graph; refs; listen; history; text; internal format)
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 (58, 1).

FORMULA

a(n) = 58*a(n-1)+a(n-2) for n>1; a(0)=29, a(1)=1683. G.f.: (29+x)/(1-58*x-x^2). [Philippe Deléham, Nov 23 2008]

a(n) = (1/2)*sqrt(842)*((29+sqrt(842))^n-(29-sqrt(842))^n)+(29/2)*((29-sqrt(842))^n+(29+sqrt(842))^n). [Paolo P. Lava, Nov 28 2008]

MATHEMATICA

Numerator[Convergents[Sqrt[842], 20]] (* or *) LinearRecurrence[{58, 1}, {29, 1683}, 20] (* Harvey P. Dale, Sep 24 2013 *)

CoefficientList[Series[(29 + x)/(1 - 58 x - x^2), {x, 0, 30}], x]  (* Vincenzo Librandi, Nov 30 2013 *)

CROSSREFS

Cf. A042625.

Sequence in context: A126555 A028478 A042627 * A190826 A045688 A084223

Adjacent sequences:  A042621 A042622 A042623 * A042625 A042626 A042627

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified June 22 08:02 EDT 2017. Contains 288605 sequences.