A041381 Denominators of continued fraction convergents to sqrt(205).

1, 3, 19, 22, 107, 129, 881, 2772, 78497, 238263, 1508075, 1746338, 8493427, 10239765, 69932017, 220035816, 6230934865, 18912840411, 119707977331, 138620817742, 674191248299, 812812066041, 5551063644545, 17466002999676, 494599147635473, 1501263445906095

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,79378,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^14 -3*x^13 +19*x^12 -22*x^11 +107*x^10 -129*x^9 +881*x^8 -2772*x^7 -881*x^6 -129*x^5 -107*x^4 -22*x^3 -19*x^2 -3*x -1) / (x^16 -79378*x^8 +1). - Colin Barker, Nov 16 2013

a(n) = 79378*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Dec 16 2013

Mathematica

Denominator[Convergents[Sqrt[205], 30]] (* Vincenzo Librandi, Dec 16 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 79378, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 3, 19, 22, 107, 129, 881, 2772, 78497, 238263, 1508075, 1746338, 8493427, 10239765, 69932017, 220035816}, 30] (* Harvey P. Dale, Apr 17 2022 *)

Prog

(Magma) I:=[1, 3, 19, 22, 107, 129, 881, 2772, 78497, 238263, 1508075, 1746338, 8493427, 10239765, 69932017, 220035816]; [n le 16 select I[n] else 79378*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 16 2013

Crossrefs

Cf. A041380, A040190.

Sequence in context: A043073 A359314 A022128 * A042231 A191074 A019408

Adjacent sequences: A041378 A041379 A041380 * A041382 A041383 A041384

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 16 2013

Status

approved