A041541 Denominators of continued fraction convergents to sqrt(287).

1, 1, 16, 17, 560, 577, 9215, 9792, 322559, 332351, 5307824, 5640175, 185793424, 191433599, 3057297409, 3248731008, 107016689665, 110265420673, 1760997999760, 1871263420433, 61641427453616, 63512690874049, 1014331790564351, 1077844481438400

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,576,0,0,0,-1).

Formula

G.f.: -(x^2-x-1)*(x^4+17*x^2+1) / (x^8-576*x^4+1). - Colin Barker, Nov 18 2013

a(n) = 576*a(n-4) - a(n-8) for n>7. - Vincenzo Librandi, Dec 19 2013

Mathematica

Denominator[Convergents[Sqrt[287], 25]] (* Harvey P. Dale, Aug 15 2011 *)
CoefficientList[Series[(1 + x - x^2) (x^4 + 17 x^2 + 1)/(x^8 - 576 x^4 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 19 2013 *)

Prog

(Magma) I:=[1, 1, 16, 17, 560, 577, 9215, 9792]; [n le 8 select I[n] else 576*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 19 2013

Crossrefs

Cf. A041540, A040270.

Sequence in context: A041538 A033052 A041540 * A041542 A030046 A002925

Adjacent sequences: A041538 A041539 A041540 * A041542 A041543 A041544

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 18 2013

Status

approved