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A041160 Numerators of continued fraction convergents to sqrt(90). 2
9, 19, 351, 721, 13329, 27379, 506151, 1039681, 19220409, 39480499, 729869391, 1499219281, 27715816449, 56930852179, 1052471155671, 2161873163521, 39966188099049, 82094249361619, 1517662676608191 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..100

Index entries for linear recurrences with constant coefficients, signature (0,38,0,-1).

FORMULA

G.f.: (1 + x)*(9 + 10*x - x^2) / (1 - 38*x^2 + x^4). [Bruno Berselli, Oct 30 2013]

a(n) = (2+(-1)^n)*((3-sqrt(10))^(n+1)+(3+sqrt(10))^(n+1))/2. [Bruno Berselli, Oct 30 2013]

MATHEMATICA

Numerator[Convergents[Sqrt[90], 30]] (* Vincenzo Librandi, Oct 29 2013 *)

Table[(2 + (-1)^n) ((3 - Sqrt[10])^(n + 1) + (3 + Sqrt[10])^(n + 1))/2, {n, 0, 30}] (* Bruno Berselli, Oct 30 2013 *)

LinearRecurrence[{0, 38, 0, -1}, {9, 19, 351, 721}, 30] (* Harvey P. Dale, May 12 2018 *)

CROSSREFS

Cf. A010541, A041161.

Sequence in context: A177179 A041677 A153316 * A248305 A089565 A001154

Adjacent sequences:  A041157 A041158 A041159 * A041161 A041162 A041163

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified January 17 20:36 EST 2020. Contains 330987 sequences. (Running on oeis4.)