A042040 Numerators of continued fraction convergents to sqrt(544).

23, 70, 793, 2449, 113447, 342790, 3884137, 11995201, 555663383, 1678985350, 19024502233, 58752492049, 2721639136487, 8223669901510, 93182008053097, 287769694060801, 13330587934849943, 40279533498610630

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,4898,0,0,0,-1).

Formula

G.f.: (23 +70*x +793*x^2 +2449*x^3 +793*x^4 -70*x^5 +23*x^6 -x^7) / ((1 -70*x^2 +x^4)*(1 +70*x^2 +x^4)). - Vincenzo Librandi, Nov 13 2013

a(n) = 4898*a(n-4) - a(n-8). - Vincenzo Librandi, Nov 14 2013

Mathematica

Numerator[Convergents[Sqrt[544], 30]] (* or *) CoefficientList[Series[(23 + 70 x + 793 x^2 + 2449 x^3 + 793 x^4 - 70 x^5 + 23 x^6 - x^7)/(1 - 4898 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 14 2013 *)
LinearRecurrence[{0, 0, 0, 4898, 0, 0, 0, -1}, {23, 70, 793, 2449, 113447, 342790, 3884137, 11995201}, 20] (* Harvey P. Dale, Jul 27 2020 *)

Prog

(Magma) I:=[23, 70, 793, 2449, 113447, 342790, 3884137, 11995201]; [n le 8 select I[n] else 4898*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 14 2013

Crossrefs

Cf. A042041.

Sequence in context: A042034 A042038 A116333 * A073035 A086104 A274050

Adjacent sequences: A042037 A042038 A042039 * A042041 A042042 A042043

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved