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A041597 Denominators of continued fraction convergents to sqrt(316). 2
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 (list; graph; refs; listen; history; text; internal format)
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: A122956 A041777 A100517 * A041030 A061104 A082381

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

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Last modified March 19 13:03 EDT 2019. Contains 321330 sequences. (Running on oeis4.)