A041153 Denominators of continued fraction convergents to sqrt(86).

1, 3, 4, 7, 11, 95, 106, 201, 307, 1122, 20503, 62631, 83134, 145765, 228899, 1976957, 2205856, 4182813, 6388669, 23348820, 426667429, 1303351107, 1730018536, 3033369643, 4763388179, 41140475075, 45903863254, 87044338329, 132948201583, 485888943078

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,20810,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^18 -3*x^17 +4*x^16 -7*x^15 +11*x^14 -95*x^13 +106*x^12 -201*x^11 +307*x^10 -1122*x^9 -307*x^8 -201*x^7 -106*x^6 -95*x^5 -11*x^4 -7*x^3 -4*x^2 -3*x-1) / (x^20-20810*x^10+1). - Colin Barker, Nov 13 2013

a(n) = 20810*a(n-10) - a(n-20). - Vincenzo Librandi, Dec 12 2013

Mathematica

Denominator/@Convergents[Sqrt[86], 50] (* Vladimir Joseph Stephan Orlovsky, Jul 05 2011 *)
CoefficientList[Series[-(x^18 - 3 x^17 + 4 x^16 - 7 x^15 + 11 x^14 - 95 x^13 + 106 x^12 - 201 x^11 + 307 x^10 - 1122 x^9 - 307 x^8 - 201 x^7 - 106 x^6 - 95 x^5 - 11 x^4 - 7 x^3 - 4 x^2 - 3 x - 1)/(x^20 - 20810 x^10 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 12 2013 *)

Prog

(Magma) I:=[1, 3, 4, 7, 11, 95, 106, 201, 307, 1122, 20503, 62631, 83134, 145765, 228899, 1976957, 2205856, 4182813, 6388669, 23348820]; [n le 20 select I[n] else 20810*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 12 2013

Crossrefs

Cf. A041152, A010159, A020843, A010537.

Sequence in context: A041901 A111518 A291853 * A041781 A042893 A132111

Adjacent sequences: A041150 A041151 A041152 * A041154 A041155 A041156

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Status

approved