A041258 Numerators of continued fraction convergents to sqrt(141).

11, 12, 83, 95, 2173, 2268, 15781, 18049, 412859, 430908, 2998307, 3429215, 78441037, 81870252, 569662549, 651532801, 14903384171, 15554916972, 108232886003, 123787802975, 2831564551453, 2955352354428

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0,0,0,190,0,0,0,-1).

Formula

G.f.: (11 +12*x +83*x^2 +95x^3 +83x^4 -12x^5 +11x^6 -x^7) / (1 -190*x^4 +x^8). - Vincenzo Librandi, Nov 01 2013

a(n) = 190*a(n-4)-a(n-8). - Vincenzo Librandi, Nov 01 2013

Mathematica

Numerator[Convergents[Sqrt[141], 30]] (* or *) CoefficientList[Series[(11 + 12 x + 83 x^2 + 95 x^3 + 83 x^4 - 12 x^5 + 11 x^6 - x^7)/(1 - 190 x^4 + x^8), {x, 0, 25}], x] (* Vincenzo Librandi, Oct 31 2013 *)

Prog

(Magma) I:=[11, 12, 83, 95, 2173, 2268, 15781, 18049]; [n le 8 select I[n] else 190*Self(n-4)-Self(n-8): n in [1..25]]; // Vincenzo Librandi, Nov 01 2013

Crossrefs

Cf. A041259.

Sequence in context: A041254 A041256 A059181 * A082262 A239463 A153070

Adjacent sequences: A041255 A041256 A041257 * A041259 A041260 A041261

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved