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A041032 Numerators of continued fraction convergents to sqrt(21). 2
4, 5, 9, 23, 32, 55, 472, 527, 999, 2525, 3524, 6049, 51916, 57965, 109881, 277727, 387608, 665335, 5710288, 6375623, 12085911, 30547445, 42633356, 73180801, 628079764, 701260565, 1329340329, 3359941223 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,110,0,0,0,0,0,-1).

FORMULA

a(n) = 110*a(n-6)-a(n-12). G.f.: -(x^11 -4*x^10 +5*x^9 -9*x^8 +23*x^7 -32*x^6 -55*x^5 -32*x^4 -23*x^3 -9*x^2 -5*x -4)/((x^4 -5*x^2 +1) *(x^8 +5*x^6 +24*x^4 +5*x^2 +1)). - Colin Barker, Jul 16 2012

MATHEMATICA

Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[21], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 17 2011 *)

Numerator[Convergents[Sqrt[21], 50]] (* Harvey P. Dale, Apr 20 2012 *)

CROSSREFS

Cf. A010477, A041033.

Sequence in context: A276645 A293282 A240926 * A041993 A153068 A075116

Adjacent sequences:  A041029 A041030 A041031 * A041033 A041034 A041035

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified August 6 00:46 EDT 2021. Contains 346493 sequences. (Running on oeis4.)