A041975 Denominators of continued fraction convergents to sqrt(510).

1, 1, 2, 5, 7, 12, 535, 547, 1082, 2711, 3793, 6504, 289969, 296473, 586442, 1469357, 2055799, 3525156, 157162663, 160687819, 317850482, 796388783, 1114239265, 1910628048, 85181873377, 87092501425, 172274374802, 431641251029, 603915625831, 1035556876860

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,542,0,0,0,0,0,-1).

Formula

G.f.: -(x^4-x^3+2*x^2+x+1)*(x^6-6*x^3-1) / (x^12-542*x^6+1). - Colin Barker, Nov 28 2013

a(n) = 542*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Dec 28 2013

Mathematica

Denominator[Convergents[Sqrt[510], 30]] (* Harvey P. Dale, Mar 03 2013 *)
CoefficientList[Series[-(x^4 - x^3 + 2 x^2 + x + 1) (x^6 - 6 x^3 - 1)/(x^12 - 542 x^6 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 28 2013 *)

Prog

(Magma) I:=[1, 1, 2, 5, 7, 12, 535, 547, 1082, 2711, 3793, 6504]; [n le 12 select I[n] else 542*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 28 2013

Crossrefs

Cf. A041974, A040487.

Sequence in context: A134472 A041203 A041517 * A042577 A092792 A238336

Adjacent sequences: A041972 A041973 A041974 * A041976 A041977 A041978

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 28 2013

Status

approved