A042508 Numerators of continued fraction convergents to sqrt(782).

27, 28, 755, 783, 43037, 43820, 1182357, 1226177, 67395915, 68622092, 1851570307, 1920192399, 105541959853, 107462152252, 2899557918405, 3007020070657, 165278641733883, 168285661804540, 4540705848651923

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,1566,0,0,0,-1).

Formula

G.f.: (27 +28*x +755*x^2 +783*x^3 +755*x^4 -28*x^5 +27*x^6 -x^7)/(1 -1566*x^4 +x^8). - Vincenzo Librandi, Nov 26 2013

a(n) = 1566*a(n-4) - a(n-8). - Vincenzo Librandi, Nov 26 2013

Mathematica

Numerator[Convergents[Sqrt[782], 30]] (* or *) CoefficientList[Series[(27 + 28 x + 755 x^2 + 783 x^3 + 755 x^4 - 28 x^5 + 27 x^6 - x^7)/(1 - 1566 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 25 2013 *)

Prog

(Magma) I:=[27, 28, 755, 783, 43037, 43820, 1182357, 1226177]; [n le 8 select I[n] else 1566*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 26 2013

Crossrefs

Cf. A042509.

Sequence in context: A042504 A042506 A041363 * A042509 A042510 A157251

Adjacent sequences: A042505 A042506 A042507 * A042509 A042510 A042511

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane

Status

approved