A041297 Denominators of continued fraction convergents to sqrt(161).

1, 1, 3, 13, 16, 45, 61, 289, 639, 928, 22911, 23839, 70589, 306195, 376784, 1059763, 1436547, 6805951, 15048449, 21854400, 539554049, 561408449, 1662370947, 7210892237, 8873263184, 24957418605, 33830681789, 160280145761, 354390973311, 514671119072

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,23550,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^18 -x^17 +3*x^16 -13*x^15 +16*x^14 -45*x^13 +61*x^12 -289*x^11 +639*x^10 -928*x^9 -639*x^8 -289*x^7 -61*x^6 -45*x^5 -16*x^4 -13*x^3 -3*x^2 -x -1) / (x^20 -23550*x^10 +1). - Colin Barker, Nov 15 2013

a(n) = 23550*a(n-10) - a(n-20). - Vincenzo Librandi, Dec 15 2013

Mathematica

Denominator[Convergents[Sqrt[161], 30]] (* Vincenzo Librandi, Dec 15 2013 *)

Prog

(Magma) I:=[1, 1, 3, 13, 16, 45, 61, 289, 639, 928, 22911, 23839, 70589, 306195, 376784, 1059763, 1436547, 6805951, 15048449, 21854400]; [n le 20 select I[n] else 23550*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 15 2013

Crossrefs

Cf. A041296, A010210.

Sequence in context: A273678 A022124 A042133 * A041815 A042589 A218364

Adjacent sequences: A041294 A041295 A041296 * A041298 A041299 A041300

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 15 2013

Status

approved