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A041840 Numerators of continued fraction convergents to sqrt(442). 2
21, 883, 37107, 1559377, 65530941, 2753858899, 115727604699, 4863313256257, 204374884367493, 8588608456690963, 360925930065387939, 15167477671202984401, 637394988120590732781, 26785756978736013761203 (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 (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]

a(n) = (21/2)*((21+sqrt(442))^n+(21-sqrt(442))^n)+(1/2)*sqrt(442)*((21+sqrt(442))^n-(21 -sqrt(442))^n). [Paolo P. Lava, Nov 28 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

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Last modified April 23 01:31 EDT 2017. Contains 285313 sequences.