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A041032 Numerators of continued fraction convergents to sqrt(21). 3
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
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
Sequence in context: A276645 A293282 A240926 * A041993 A153068 A075116
KEYWORD
nonn,cofr,frac,easy
AUTHOR
STATUS
approved

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Last modified March 29 11:14 EDT 2024. Contains 371278 sequences. (Running on oeis4.)