A041073 Denominators of continued fraction convergents to sqrt(43).

1, 1, 2, 7, 9, 52, 61, 235, 296, 531, 6668, 7199, 13867, 48800, 62667, 362135, 424802, 1636541, 2061343, 3697884, 46435951, 50133835, 96569786, 339843193, 436412979, 2521908088, 2958321067, 11396871289, 14355192356, 25752063645, 323379956096, 349132019741

Offset

0,3

Links

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

Les Tablettes du Chercheur, Problem 364, pp. 11, Mai 15 1891.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,6964,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^18 -x^17 +2*x^16 -7*x^15 +9*x^14 -52*x^13 +61*x^12 -235*x^11 +296*x^10 -531*x^9 -296*x^8 -235*x^7 -61*x^6 -52*x^5 -9*x^4 -7*x^3 -2*x^2 -x -1) / (x^20 -6964*x^10 +1). - Colin Barker, Nov 12 2013

a(n) = 6964*a(n-10) - a(n-20). - Vincenzo Librandi, Dec 10 2013

Mathematica

Denominator[Convergents[Sqrt[43], 40]] (* Vincenzo Librandi, Dec 10 2013 *)

Prog

(Magma) I:=[1, 1, 2, 7, 9, 52, 61, 235, 296, 531, 6668, 7199, 13867, 48800, 62667, 362135, 424802, 1636541, 2061343, 3697884]; [n le 20 select I[n] else 6964*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 10 2013

Crossrefs

Cf. A010497, A041072.

Sequence in context: A360734 A041717 A002353 * A079942 A272412 A042561

Adjacent sequences: A041070 A041071 A041072 * A041074 A041075 A041076

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 12 2013

Status

approved