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A041599 Denominators of continued fraction convergents to sqrt(317). 2
1, 1, 5, 41, 46, 133, 312, 445, 3872, 15933, 19805, 689303, 709108, 3525735, 28914988, 32440723, 93796434, 220033591, 313830025, 2730673791, 11236525189, 13967198980, 486121290509, 500088489489, 2486475248465, 20391890477209, 22878365725674, 66148621928557 (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 (0,0,0,0,0,0,0,0,0,0,705236,0,0,0,0,0,0,0,0,0,0,1).

FORMULA

G.f.: -(x^20 -x^19 +5*x^18 -41*x^17 +46*x^16 -133*x^15 +312*x^14 -445*x^13 +3872*x^12 -15933*x^11 +19805*x^10 +15933*x^9 +3872*x^8 +445*x^7 +312*x^6 +133*x^5 +46*x^4 +41*x^3 +5*x^2 +x +1) / (x^22 +705236*x^11 -1). - Colin Barker, Nov 19 2013

a(n) = 705236*a(n-11) + a(n-22) for n>21. - Vincenzo Librandi, Dec 21 2013

MATHEMATICA

Denominator[Convergents[Sqrt[317], 30]] (* Vincenzo Librandi Dec 21 2013 *)

PROG

(MAGMA) I:=[1, 1, 5, 41, 46, 133, 312, 445, 3872, 15933, 19805, 689303, 709108, 3525735, 28914988, 32440723, 93796434, 220033591, 313830025, 2730673791, 11236525189, 13967198980]; [n le 22 select I[n] else 705236*Self(n-11)+Self(n-22): n in [1..40]]; // Vincenzo Librandi, Dec 21 2013

CROSSREFS

Cf. A041598, A040299.

Sequence in context: A003084 A010573 A043083 * A232881 A174054 A106963

Adjacent sequences:  A041596 A041597 A041598 * A041600 A041601 A041602

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 May 24 03:21 EDT 2017. Contains 286937 sequences.