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A041182 Numerators of continued fraction convergents to sqrt(102). 2
10, 101, 2030, 20401, 410050, 4120901, 82828070, 832401601, 16730860090, 168141002501, 3379550910110, 33963650103601, 682652552982130, 6860489179924901, 137892436151480150, 1385784850694726401 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Vincenzo Librandi and Bruno Berselli, Table of n, a(n) for n = 0..100 (first 66 terms from Vincenzo Librandi).

Index entries for linear recurrences with constant coefficients, signature (0,202,0,-1).

FORMULA

G.f.: (10 + 101*x + 10*x^2 - x^3)/(1 - 202*x^2 + x^4). [Bruno Berselli, Oct 30 2013]

a(n) = 202*a(n-2)-a(n-4). [Bruno Berselli, Oct 30 2013]

MATHEMATICA

Numerator[Convergents[Sqrt[102], 30]] (* Vincenzo Librandi, Oct 30 2013 *)

RecurrenceTable[{a[0] == 10, a[1] == 101, a[2] == 2030, a[3] == 20401, a[n] == 202 a[n - 2] - a[n - 4]}, a, {n, 0, 15}] (* Bruno Berselli, Oct 30 2013 *)

CROSSREFS

Cf. A041183.

Sequence in context: A309802 A324083 A162849 * A036299 A061107 A015498

Adjacent sequences:  A041179 A041180 A041181 * A041183 A041184 A041185

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified November 17 18:24 EST 2019. Contains 329241 sequences. (Running on oeis4.)