A041237 Denominators of continued fraction convergents to sqrt(130).

1, 2, 5, 112, 229, 570, 12769, 26108, 64985, 1455778, 2976541, 7408860, 165971461, 339351782, 844675025, 18922202332, 38689079689, 96300361710, 2157297037309, 4410894436328, 10979085909965, 245950784455558, 502880654821081, 1251712094097720

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,114,0,0,1).

Formula

G.f.: -(x^4-2*x^3+5*x^2+2*x+1) / (x^6+114*x^3-1). - Colin Barker, Nov 14 2013

a(n) = 114*a(n-3) + a(n-6). - Vincenzo Librandi, Dec 13 2013

Mathematica

Denominator[Convergents[Sqrt[130], 30]] (* Vincenzo Librandi, Dec 13 2013 *)

Prog

(Magma) I:=[ 1, 2, 5, 112, 229, 570 ]; [n le 6 select I[n] else 114*Self(n-3)+Self(n-6): n in [1..40]]; // Vincenzo Librandi, Dec 13 2013

Crossrefs

Cf. A041236, A040118.

Sequence in context: A023263 A070855 A228850 * A221476 A015172 A132526

Adjacent sequences: A041234 A041235 A041236 * A041238 A041239 A041240

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 14 2013

Status

approved