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A041589 Denominators of continued fraction convergents to sqrt(312). 2
1, 1, 2, 3, 104, 107, 211, 318, 11023, 11341, 22364, 33705, 1168334, 1202039, 2370373, 3572412, 123832381, 127404793, 251237174, 378641967, 13125064052, 13503706019, 26628770071, 40132476090, 1391132957131, 1431265433221, 2822398390352, 4253663823573 (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 (0,0,0,106,0,0,0,-1).

FORMULA

G.f.: -(x^2-x-1)*(x^4+3*x^2+1) / (x^8-106*x^4+1). - Colin Barker, Nov 19 2013

a(n) = 106*a(n-4) - a(n-8) for n>7. - Vincenzo Librandi, Dec 20 2013

MATHEMATICA

Denominator/@Convergents[Sqrt[312], 30] (* Harvey P. Dale, Jun 04 2011 *)

CoefficientList[Series[(1 + x - x^2) (x^4 + 3 x^2 + 1)/(x^8 - 106 x^4 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 20 2013 *)

PROG

(MAGMA) I:=[1, 1, 2, 3, 104, 107, 211, 318]; [n le 8 select I[n] else 106*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 20 2013

CROSSREFS

Cf. A041588, A040294.

Sequence in context: A249409 A256114 A062657 * A039768 A097653 A164926

Adjacent sequences:  A041586 A041587 A041588 * A041590 A041591 A041592

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 February 22 15:49 EST 2019. Contains 320399 sequences. (Running on oeis4.)