A042424 Numerators of continued fraction convergents to sqrt(740).

27, 109, 136, 1741, 1877, 9249, 501323, 2014541, 2515864, 32204909, 34720773, 171088001, 9273472827, 37264979309, 46538452136, 595726404941, 642264857077, 3164785833249, 171540699852523

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,18498,0,0,0,0,0,-1).

Formula

G.f.: (27 + 109*x + 136*x^2 + 1741*x^3 + 1877*x^4 + 9249*x^5 + 1877*x^6 - 1741*x^7 + 136*x^8 - 109*x^9 + 27*x^10 - x^11)/(1 - 18498*x^6 + x^12). - Vincenzo Librandi, Nov 24 2013

a(n) = 18498*a(n-6) - a(n-12). - Vincenzo Librandi, Nov 24 2013

Mathematica

Numerator[Convergents[Sqrt[740], 30]] (* or *) CoefficientList[Series[(27 + 109 x + 136 x^2 + 1741 x^3 + 1877 x^4 + 9249 x^5 + 1877 x^6 - 1741 x^7 + 136 x^8 - 109 x^9 + 27 x^10 - x^11)/(1 - 18498 x^6 + x^12), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 24 2013 *)

Prog

(Magma) I:=[27, 109, 136, 1741, 1877, 9249, 501323, 2014541, 2515864, 32204909, 34720773, 171088001]; [n le 12 select I[n] else 18498*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Nov 24 2013

Crossrefs

Cf. A042425.

Sequence in context: A134171 A129026 A042426 * A248095 A193391 A193399

Adjacent sequences: A042421 A042422 A042423 * A042425 A042426 A042427

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane

Status

approved