A041537 Denominators of continued fraction convergents to sqrt(285).

1, 1, 8, 17, 127, 144, 4735, 4879, 38888, 82655, 617473, 700128, 23021569, 23721697, 189073448, 401868593, 3002153599, 3404022192, 111930863743, 115334885935, 919275065288, 1953885016511, 14596470180865, 16550355197376, 544207836496897, 560758191694273

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, 4862, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^10 -x^9 +8*x^8 -17*x^7 +127*x^6 -144*x^5 -127*x^4 -17*x^3 -8*x^2 -x -1) / ((x^4 -17*x^2 +1)*(x^8 +17*x^6 +288*x^4 +17*x^2 +1)). - Colin Barker, Nov 18 2013

a(n) = 4862*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Dec 19 2013

Mathematica

Denominator[Convergents[Sqrt[285], 30]] (* Harvey P. Dale, Nov 08 2013 *)
CoefficientList[Series[-(x^10 - x^9 + 8 x^8 - 17 x^7 + 127 x^6 - 144 x^5 - 127 x^4 - 17 x^3 - 8 x^2 - x - 1)/((x^4 - 17 x^2 + 1) (x^8 + 17 x^6 + 288 x^4 + 17 x^2 + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 19 2013 *)

Prog

(Magma) I:=[1, 1, 8, 17, 127, 144, 4735, 4879, 38888, 82655, 617473, 700128]; [n le 12 select I[n] else 4862*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 19 2013

Crossrefs

Cf. A041536, A176104, A040268.

Sequence in context: A097405 A192282 A088588 * A153315 A041126 A248289

Adjacent sequences: A041534 A041535 A041536 * A041538 A041539 A041540

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 18 2013

Status

approved