A041469 Denominators of continued fraction convergents to sqrt(250).

1, 1, 5, 16, 53, 228, 281, 8658, 8939, 44414, 142181, 470957, 2026009, 2496966, 76934989, 79431955, 394662809, 1263420382, 4184923955, 18003116202, 22188040157, 683644320912, 705832361069, 3506973765188, 11226753656633, 37187234735087, 159975692596981

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,8886,0,0,0,0,0,0,1).

Formula

G.f.: -(x^12 -x^11 +5*x^10 -16*x^9 +53*x^8 -228*x^7 +281*x^6 +228*x^5 +53*x^4 +16*x^3 +5*x^2 +x +1) / (x^14 +8886*x^7 -1). - Colin Barker, Nov 18 2013

a(n) = 8886*a(n-7) + a(n-14) for n>13. - Vincenzo Librandi, Dec 18 2013

Mathematica

Denominator[Convergents[Sqrt[250], 30]] (* Vincenzo Librandi, Dec 18 2013 *)

Prog

(Magma) I:=[1, 1, 5, 16, 53, 228, 281, 8658, 8939, 44414, 142181, 470957, 2026009, 2496966]; [n le 14 select I[n] else 8886*Self(n-7)+Self(n-14): n in [1..40]]; // Vincenzo Librandi, Dec 18 2013

Crossrefs

Cf. A041468, A040234.

Sequence in context: A347434 A173871 A108300 * A089102 A098912 A299685

Adjacent sequences: A041466 A041467 A041468 * A041470 A041471 A041472

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 18 2013

Status

approved