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A041693 Denominators of continued fraction convergents to sqrt(366). 2
1, 7, 8, 15, 23, 61, 755, 1571, 2326, 3897, 6223, 47458, 1809627, 12714847, 14524474, 27239321, 41763795, 110766911, 1370966727, 2852700365, 4223667092, 7076367457, 11300034549, 86176609300, 3286011187949, 23088254924943, 26374266112892, 49462521037835 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,1815850,0,0,0,0,0,0,0,0,0,0,0,-1).

FORMULA

G.f.: -(x^22 -7*x^21 +8*x^20 -15*x^19 +23*x^18 -61*x^17 +755*x^16 -1571*x^15 +2326*x^14 -3897*x^13 +6223*x^12 -47458*x^11 -6223*x^10 -3897*x^9 -2326*x^8 -1571*x^7 -755*x^6 -61*x^5 -23*x^4 -15*x^3 -8*x^2 -7*x-1)/(x^24 -1815850*x^12 +1). - Vincenzo Librandi, Dec 23 2013

a(n) = 1815850*a(n-12) - a(n-24) for n>23. - Vincenzo Librandi, Dec 23 2013

MATHEMATICA

Denominator[Convergents[Sqrt[366], 30]] (* or *) CoefficientList[Series[-(x^22 - 7 x^21 + 8 x^20 - 15 x^19 + 23 x^18 - 61 x^17 + 755 x^16 - 1571 x^15 + 2326 x^14 - 3897 x^13 + 6223 x^12 - 47458 x^11 - 6223 x^10 - 3897 x^9 - 2326 x^8 - 1571 x^7 - 755 x^6 - 61 x^5 - 23 x^4 - 15 x^3 - 8 x^2 - 7 x - 1)/(x^24 - 1815850 x^12 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 23 2013 *)

PROG

(MAGMA) I:=[1, 7, 8, 15, 23, 61, 755, 1571, 2326, 3897, 6223, 47458, 1809627, 12714847, 14524474, 27239321, 41763795, 110766911, 1370966727, 2852700365, 4223667092, 7076367457, 11300034549, 86176609300]; [n le 24 select I[n] else 1815850*Self(n-12)-Self(n-24): n in [1..40]]; // Vincenzo Librandi, Dec 23 2013

CROSSREFS

Cf. A041692.

Sequence in context: A022097 A041100 A129658 * A042001 A020690 A191413

Adjacent sequences:  A041690 A041691 A041692 * A041694 A041695 A041696

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Vincenzo Librandi, Dec 23 2013

STATUS

approved

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Last modified December 13 09:05 EST 2017. Contains 295957 sequences.