A042292 Numerators of continued fraction convergents to sqrt(672).

25, 26, 311, 337, 17161, 17498, 209639, 227137, 11566489, 11793626, 141296375, 153090001, 7795796425, 7948886426, 95233547111, 103182433537, 5254355223961, 5357537657498, 64187269456439

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,674,0,0,0,-1).

Formula

G.f.: (25 +26*x +311*x^2 +337*x^3 +311*x^4 -26*x^5 +25*x^6 -x^7)/(1 -674*x^4 +x^8). - Vincenzo Librandi, Nov 21 2013

a(n) = 674*a(n-4) - a(n-8). - Vincenzo Librandi, Nov 21 2013

Mathematica

Numerator[Convergents[Sqrt[672], 30]] (* or *) CoefficientList[Series[(25 + 26 x + 311 x^2 + 337 x^3 + 311 x^4 - 26 x^5 + 25 x^6 - x^7)/(1 - 674 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 21 2013 *)

Prog

(Magma) I:=[25, 26, 311, 337, 17161, 17498, 209639, 227137]; [n le 8 select I[n] else 674*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 21 2013

Crossrefs

Cf. A042293.

Sequence in context: A042286 A042288 A042290 * A042294 A041311 A042296

Adjacent sequences: A042289 A042290 A042291 * A042293 A042294 A042295

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved