A042296 Numerators of continued fraction convergents to sqrt(674).

25, 26, 649, 675, 34399, 35074, 876175, 911249, 46438625, 47349874, 1182835601, 1230185475, 62692109351, 63922294826, 1596827185175, 1660749480001, 84634301185225, 86295050665226, 2155715517150649

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,1350,0,0,0,-1).

Formula

G.f.: (25 +26*x +649*x^2 +675*x^3 +649*x^4 -26*x^5 +25*x^6 -x^7)/(1 -1350*x^4 +x^8). - Vincenzo Librandi, Nov 21 2013

a(n) = 1350*a(n-4) - a(n-8). - Vincenzo Librandi, Nov 21 2013

Mathematica

Numerator[Convergents[Sqrt[674], 30]] (* or *) CoefficientList[Series[(25 + 26 x + 649 x^2 + 675 x^3 + 649 x^4 - 26 x^5 + 25 x^6 - x^7)/(1 - 1350 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 21 2013 *)
LinearRecurrence[{0, 0, 0, 1350, 0, 0, 0, -1}, {25, 26, 649, 675, 34399, 35074, 876175, 911249}, 20] (* Harvey P. Dale, Jul 01 2017 *)

Prog

(Magma) I:=[25, 26, 649, 675, 34399, 35074, 876175, 911249]; [n le 8 select I[n] else 1350*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 21 2013

Crossrefs

Cf. A042297.

Sequence in context: A042292 A042294 A041311 * A042297 A042298 A157091

Adjacent sequences: A042293 A042294 A042295 * A042297 A042298 A042299

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved