A042504 Numerators of continued fraction convergents to sqrt(780).

27, 28, 363, 391, 21477, 21868, 283893, 305761, 16794987, 17100748, 222003963, 239104711, 13133658357, 13372763068, 173606815173, 186979578241, 10270504040187, 10457483618428, 135760307461323

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,782,0,0,0,-1).

Formula

G.f.: (27 +28*x +363*x^2 +391*x^3 +363*x^4 -28*x^5 +27*x^6 -x^7)/(1 -782*x^4 +x^8). - Vincenzo Librandi, Nov 26 2013

a(n) = 782*a(n-4) - a(n-8). - Vincenzo Librandi, Nov 26 2013

Mathematica

Numerator[Convergents[Sqrt[780], 20]] (* Harvey P. Dale, Oct 10 2011 *)
CoefficientList[Series[(27 + 28 x + 363 x^2 + 391 x^3 + 363 x^4 - 28 x^5 +27 x^6 - x^7)/(1 - 782 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 26 2013 *)

Prog

(Magma) I:=[27, 28, 363, 391, 21477, 21868, 283893, 305761]; [n le 8 select I[n] else 782*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 26 2013

Crossrefs

Cf. A042505.

Sequence in context: A042498 A042500 A042502 * A042506 A041363 A042508

Adjacent sequences: A042501 A042502 A042503 * A042505 A042506 A042507

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved