A041497 Denominators of continued fraction convergents to sqrt(265).

1, 3, 4, 7, 18, 43, 61, 104, 373, 12040, 36493, 48533, 85026, 218585, 522196, 740781, 1262977, 4529712, 146213761, 443170995, 589384756, 1032555751, 2654496258, 6341548267, 8996044525, 15337592792, 55008822901, 1775619925624, 5381868599773, 7157488525397

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,12144,0,0,0,0,0,0,0,0,1).

Formula

G.f.: -(x^16 -3*x^15 +4*x^14 -7*x^13 +18*x^12 -43*x^11 +61*x^10 -104*x^9 +373*x^8 +104*x^7 +61*x^6 +43*x^5 +18*x^4 +7*x^3 +4*x^2 +3*x +1) / (x^18 +12144*x^9 -1). - Colin Barker, Nov 18 2013

a(n) = 12144*a(n-9) + a(n-18) for n>17, - Vincenzo Librandi, Dec 19 2013

Mathematica

Denominator[Convergents[Sqrt[265], 30]] (* Vincenzo Librandi, Dec 19 2013 *)

Prog

(Magma) I:=[1, 3, 4, 7, 18, 43, 61, 104, 373, 12040, 36493, 48533, 85026, 218585, 522196, 740781, 1262977, 4529712]; [n le 18 select I[n] else 12144*Self(n-9)+Self(n-18): n in [1..30]]; // Vincenzo Librandi, Dec 19 2013

Crossrefs

Cf. A041496, A040248.

Sequence in context: A258740 A109749 A307738 * A042227 A117789 A169892

Adjacent sequences: A041494 A041495 A041496 * A041498 A041499 A041500

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 18 2013

Status

approved