A042732 Numerators of continued fraction convergents to sqrt(896).

29, 30, 419, 449, 26461, 26910, 376291, 403201, 23761949, 24165150, 337908899, 362074049, 21338203741, 21700277790, 303441815011, 325142092801, 19161683197469, 19486825290270, 272490411970979, 291977237261249, 17207170173123421, 17499147410384670, 244696086508124131

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,898,0,0,0,-1).

Formula

G.f.: (29 +30*x +419*x^2 +449*x^3 +419*x^4 -30*x^5 +29*x^6 -x^7)/(1 -898*x^4 +x^8). - Vincenzo Librandi, Dec 03 2013

a(n) = 898*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 03 2013

Mathematica

Numerator[Convergents[Sqrt[896], 30]] (* or *) CoefficientList[Series[(29 + 30 x + 419 x^2 + 449 x^3 + 419 x^4 - 30 x^5 + 29 x^6 - x^7)/(1 - 898 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 03 2013 *)
LinearRecurrence[{0, 0, 0, 898, 0, 0, 0, -1}, {29, 30, 419, 449, 26461, 26910, 376291, 403201}, 30] (* Harvey P. Dale, Apr 02 2018 *)

Prog

(Magma) I:=[29, 30, 419, 449, 26461, 26910, 376291, 403201]; [n le 8 select I[n] else 898*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Dec 03 2013

Crossrefs

Cf. A042733.

Sequence in context: A042726 A042728 A042730 * A042734 A041419 A042736

Adjacent sequences: A042729 A042730 A042731 * A042733 A042734 A042735

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Vincenzo Librandi, Dec 03 2013

Status

approved