A041597 Denominators of continued fraction convergents to sqrt(316).

1, 1, 4, 9, 76, 161, 559, 720, 25039, 25759, 102316, 230391, 1945444, 4121279, 14309281, 18430560, 640948321, 659378881, 2619084964, 5897548809, 49799475436, 105496499681, 366288974479, 471785474160, 16406995095919, 16878780570079, 67043336806156

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,25598,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^14 -x^13 +4*x^12 -9*x^11 +76*x^10 -161*x^9 +559*x^8 -720*x^7 -559*x^6 -161*x^5 -76*x^4 -9*x^3 -4*x^2 -x -1) / ((x^8 -160*x^4 +1)*(x^8 +160*x^4 +1)). - Colin Barker, Nov 19 2013

a(n) = 25598*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Dec 21 2013

Mathematica

Denominator[Convergents[Sqrt[316], 30]] (* Vincenzo Librandi Dec 21 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 25598, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 1, 4, 9, 76, 161, 559, 720, 25039, 25759, 102316, 230391, 1945444, 4121279, 14309281, 18430560}, 30] (* Harvey P. Dale, Mar 21 2017 *)

Prog

(Magma) I:=[1, 1, 4, 9, 76, 161, 559, 720, 25039, 25759, 102316, 230391, 1945444, 4121279, 14309281, 18430560]; [n le 16 select I[n] else 25598*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 21 2013

Crossrefs

Cf. A041596, A040298.

Sequence in context: A367276 A100517 A327579 * A041030 A361067 A359654

Adjacent sequences: A041594 A041595 A041596 * A041598 A041599 A041600

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 19 2013

Status

approved