A042700 Numerators of continued fraction convergents to sqrt(880).

29, 30, 59, 89, 5221, 5310, 10531, 15841, 929309, 945150, 1874459, 2819609, 165411781, 168231390, 333643171, 501874561, 29442367709, 29944242270, 59386609979, 89330852249, 5240576040421, 5329906892670

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,178,0,0,0,-1).

Formula

G.f.: (29 +30*x +59*x^2 +89*x^3 +59*x^4 -30*x^5 +29*x^6 -x^7)/(1 -178*x^4 +x^8). - Vincenzo Librandi, Dec 02 2013

a(n) = 178*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 02 2013

Mathematica

Numerator[Convergents[Sqrt[880], 30]]
(* or *)
CoefficientList[Series[(29 + 30 x + 59 x^2 + 89 x^3 + 59 x^4 - 30 x^5 + 29 x^6 - x^7)/(1 - 178 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 02 2013 *)
LinearRecurrence[{0, 0, 0, 178, 0, 0, 0, -1}, {29, 30, 59, 89, 5221, 5310, 10531, 15841}, 30] (* Harvey P. Dale, Mar 27 2022 *)

Prog

(Magma) I:=[29, 30, 59, 89, 5221, 5310, 10531, 15841]; [n le 8 select I[n] else 178*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Dec 02 2013

Crossrefs

Cf. A042701.

Sequence in context: A042694 A042696 A042698 * A042690 A042692 A042688

Adjacent sequences: A042697 A042698 A042699 * A042701 A042702 A042703

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved