A041323 Denominators of continued fraction convergents to sqrt(175).

1, 4, 9, 13, 35, 153, 4013, 16205, 36423, 52628, 141679, 619344, 16244623, 65597836, 147440295, 213038131, 573516557, 2507104359, 65758229891, 265540023923, 596838277737, 862378301660, 2321594881057, 10148757825888, 266189298354145, 1074905951242468

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,4048,0,0,0,0,0,-1).

Formula

G.f.: -(x^10 -4*x^9 +9*x^8 -13*x^7 +35*x^6 -153*x^5 -35*x^4 -13*x^3 -9*x^2 -4*x -1) / ((x^4 -16*x^2 +1)*(x^8 +16*x^6 +255*x^4 +16*x^2 +1)). - Colin Barker, Nov 15 2013

a(n) = 4048*a(n-6) - a(n-12). - Vincenzo Librandi, Dec 15 2013

Mathematica

Denominator[Convergents[Sqrt[175], 30]] (* Vincenzo Librandi, Dec 15 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 4048, 0, 0, 0, 0, 0, -1}, {1, 4, 9, 13, 35, 153, 4013, 16205, 36423, 52628, 141679, 619344}, 30] (* Harvey P. Dale, Jan 11 2024 *)

Prog

(Magma) I:=[1, 4, 9, 13, 35, 153, 4013, 16205, 36423, 52628, 141679, 619344]; [n le 12 select I[n] else 4048*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 15 2013

Crossrefs

Cf. A041322, A010219.

Sequence in context: A333848 A063606 A033287 * A319217 A041028 A041211

Adjacent sequences: A041320 A041321 A041322 * A041324 A041325 A041326

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 15 2013

Status

approved