A041251 Denominators of continued fraction convergents to sqrt(137).

1, 1, 3, 7, 10, 17, 44, 105, 149, 3383, 3532, 10447, 24426, 34873, 59299, 153471, 366241, 519712, 11799905, 12319617, 36439139, 85197895, 121637034, 206834929, 535306892, 1277448713, 1812755605, 41158072023, 42970827628, 127099727279, 297170282186

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,3488,0,0,0,0,0,0,0,0,1).

Formula

G.f.: -(x^16 -x^15 +3*x^14 -7*x^13 +10*x^12 -17*x^11 +44*x^10 -105*x^9 +149*x^8 +105*x^7 +44*x^6 +17*x^5 +10*x^4 +7*x^3 +3*x^2 +x +1) / (x^18 +3488*x^9 -1). - Colin Barker, Nov 14 2013

a(n) = 3488*a(n-9) + a(n-18). - Vincenzo Librandi, Dec 13 2013

Mathematica

Denominator[Convergents[Sqrt[137], 30]]  (* Vincenzo Librandi, Dec 13 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 3488, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {1, 1, 3, 7, 10, 17, 44, 105, 149, 3383, 3532, 10447, 24426, 34873, 59299, 153471, 366241, 519712}, 40] (* Harvey P. Dale, Oct 29 2022 *)

Prog

(Magma) I:=[1, 1, 3, 7, 10, 17, 44, 105, 149, 3383, 3532, 10447, 24426, 34873, 59299, 153471, 366241, 519712]; [n le 18 select I[n] else 3488*Self(n-9)+Self(n-18): n in [1..40]]; // Vincenzo Librandi, Dec 13 2013

Crossrefs

Cf. A041250, A010196.

Sequence in context: A304216 A305247 A316547 * A042435 A042591 A098001

Adjacent sequences: A041248 A041249 A041250 * A041252 A041253 A041254

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 14 2013

Status

approved