A041435 Denominators of continued fraction convergents to sqrt(233).

1, 3, 4, 15, 19, 34, 53, 87, 314, 401, 1517, 45911, 139250, 185161, 694733, 879894, 1574627, 2454521, 4029148, 14541965, 18571113, 70255304, 2126230233, 6448946003, 8575176236, 32174474711, 40749650947, 72924125658, 113673776605, 186597902263, 673467483394

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, 0, 46312, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Formula

G.f.: -(x^20 -3*x^19 +4*x^18 -15*x^17 +19*x^16 -34*x^15 +53*x^14 -87*x^13 +314*x^12 -401*x^11 +1517*x^10 +401*x^9 +314*x^8 +87*x^7 +53*x^6 +34*x^5 +19*x^4 +15*x^3 +4*x^2 +3*x +1) / (x^22 +46312*x^11 -1). - Colin Barker, Nov 17 2013

a(n) = 46312*a(n-11) + a(n-22) for n>21. - Vincenzo Librandi, Dec 17 2013

Mathematica

Denominator[Convergents[Sqrt[233], 30]] (* Vincenzo Librandi, Dec 17 2013 *)

Prog

(Magma) I:=[1, 3, 4, 15, 19, 34, 53, 87, 314, 401, 1517, 45911, 139250, 185161, 694733, 879894, 1574627, 2454521, 4029148, 14541965, 18571113, 70255304]; [n le 22 select I[n] else 46312*Self(n-11)+Self(n-22): n in [1..40]]; // Vincenzo Librandi, Dec 17 2013

Crossrefs

Cf. A041434, A040217.

Sequence in context: A053359 A056742 A338123 * A136210 A041819 A369910

Adjacent sequences: A041432 A041433 A041434 * A041436 A041437 A041438

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 17 2013

Status

approved