A041182 Numerators of continued fraction convergents to sqrt(102).

10, 101, 2030, 20401, 410050, 4120901, 82828070, 832401601, 16730860090, 168141002501, 3379550910110, 33963650103601, 682652552982130, 6860489179924901, 137892436151480150, 1385784850694726401

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