A041627 Denominators of continued fraction convergents to sqrt(332).

1, 4, 5, 9, 77, 86, 163, 738, 26731, 107662, 134393, 242055, 2070833, 2312888, 4383721, 19847772, 718903513, 2895461824, 3614365337, 6509827161, 55692982625, 62202809786, 117895792411, 533785979430, 19334191051891, 77870550186994, 97204741238885

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, 26894, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^14 -4*x^13 +5*x^12 -9*x^11 +77*x^10 -86*x^9 +163*x^8 -738*x^7 -163*x^6 -86*x^5 -77*x^4 -9*x^3 -5*x^2 -4*x -1) / ((x^8 -164*x^4 +1)*(x^8 +164*x^4 +1)). - Colin Barker, Nov 20 2013

a(n) = 26894*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Dec 22 2013

Mathematica

Denominator[Convergents[Sqrt[332], 30]] (* Vincenzo Librandi, Dec 22 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 26894, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 4, 5, 9, 77, 86, 163, 738, 26731, 107662, 134393, 242055, 2070833, 2312888, 4383721, 19847772}, 30] (* Harvey P. Dale, Mar 03 2024 *)

Prog

(Magma) I:=[1, 4, 5, 9, 77, 86, 163, 738, 26731, 107662, 134393, 242055, 2070833, 2312888, 4383721, 19847772]; [n le 16 select I[n] else 26894*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 22 2013

Crossrefs

Cf. A041626, A040313.

Sequence in context: A041467 A180436 A121919 * A132811 A042179 A042427

Adjacent sequences: A041624 A041625 A041626 * A041628 A041629 A041630

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 20 2013

Status

approved