A041195 Denominators of continued fraction convergents to sqrt(108).

1, 2, 3, 5, 23, 28, 51, 130, 2651, 5432, 8083, 13515, 62143, 75658, 137801, 351260, 7163001, 14677262, 21840263, 36517525, 167910363, 204427888, 372338251, 949104390, 19354426051, 39657956492, 59012382543, 98670339035, 453693738683, 552364077718

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,2702,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^14 -2*x^13 +3*x^12 -5*x^11 +23*x^10 -28*x^9 +51*x^8 -130*x^7 -51*x^6 -28*x^5 -23*x^4 -5*x^3 -3*x^2 -2*x -1) / ((x^8 -52*x^4 +1)*(x^8 +52*x^4 +1)). - Colin Barker, Nov 14 2013

a(n) = 2702*a(n-8) - a(n-16). - Vincenzo Librandi, Dec 12 2013

Mathematica

Denominator[Convergents[Sqrt[108], 30]] (* Vincenzo Librandi, Dec 12 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 2702, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 2, 3, 5, 23, 28, 51, 130, 2651, 5432, 8083, 13515, 62143, 75658, 137801, 351260}, 30] (* Harvey P. Dale, Jan 08 2016 *)

Prog

(Magma) I:=[1, 2, 3, 5, 23, 28, 51, 130, 2651, 5432, 8083, 13515, 62143, 75658, 137801, 351260]; [n le 16 select I[n] else 2702*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 12 2013

Crossrefs

Cf. A041194, A010174.

Sequence in context: A024782 A024775 A024767 * A042141 A122004 A023231

Adjacent sequences: A041192 A041193 A041194 * A041196 A041197 A041198

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 14 2013

Status

approved