A042224 Numerators of continued fraction convergents to sqrt(638).

25, 76, 101, 682, 1465, 9472, 10937, 42283, 2125087, 6417544, 8542631, 57673330, 123889291, 801009076, 924898367, 3575704177, 179710107217, 542706025828, 722416133045, 4877202824098, 10476821781241, 67738133511544, 78214955292785, 302382999389899

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, 0, 0, 0, 0, 84566, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^15 -25*x^14 +76*x^13 -101*x^12 +682*x^11 -1465*x^10 +9472*x^9 -10937*x^8 -42283*x^7 -10937*x^6 -9472*x^5 -1465*x^4 -682*x^3 -101*x^2 -76*x -25) / (x^16 -84566*x^8 +1). - Colin Barker, Dec 04 2013

Mathematica

Numerator[Convergents[Sqrt[638], 30]] (* Vincenzo Librandi, Nov 19 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 84566, 0, 0, 0, 0, 0, 0, 0, -1}, {25, 76, 101, 682, 1465, 9472, 10937, 42283, 2125087, 6417544, 8542631, 57673330, 123889291, 801009076, 924898367, 3575704177}, 30] (* Harvey P. Dale, Aug 28 2023 *)

Crossrefs

Cf. A042225, A040612.

Sequence in context: A118610 A008852 A042226 * A042228 A042230 A189642

Adjacent sequences: A042221 A042222 A042223 * A042225 A042226 A042227

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 04 2013

Status

approved