A041305 Denominators of continued fraction convergents to sqrt(165).

1, 1, 6, 13, 71, 84, 2087, 2171, 12942, 28055, 153217, 181272, 4503745, 4685017, 27928830, 60542677, 330642215, 391184892, 9719079623, 10110264515, 60270402198, 130651068911, 713525746753, 844176815664, 20973769322689, 21817946138353

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,2158,0,0,0,0,0,-1).

Formula

G.f.: -(x^10 -x^9 +6*x^8 -13*x^7 +71*x^6 -84*x^5 -71*x^4 -13*x^3 -6*x^2 -x -1) / ((x^4 -13*x^2 +1)*(x^8 +13*x^6 +168*x^4 +13*x^2 +1)). - Colin Barker, Nov 15 2013

a(n) = 2158*a(n-6) - a(n-12). - Vincenzo Librandi, Dec 15 2013

Mathematica

Denominator[Convergents[Sqrt[165], 30]] (* Vincenzo Librandi, Dec 15 2013 *)

Prog

(Magma) I:=[1, 1, 6, 13, 71, 84, 2087, 2171, 12942, 28055, 153217, 181272]; [n le 12 select I[n] else 2158*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 15 2013

Crossrefs

Cf. A041304, A010213, A178592.

Sequence in context: A177175 A301605 A119110 * A215755 A144535 A042641

Adjacent sequences: A041302 A041303 A041304 * A041306 A041307 A041308

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 15 2013

Status

approved