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

Author

N. J. A. Sloane

Keywords

• nonn
• frac
• easy

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).

Crossrefs

Cf. A041304, A010213, A178592.

Programs

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

Mathematica

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

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

Extensions

More terms from Colin Barker, Nov 15 2013