A041076 -id:A041076 - cp's OEIS frontend

A010135 Continued fraction for sqrt(45).

6, 1, 2, 2, 2, 1, 12, 1, 2, 2, 2, 1, 12, 1, 2, 2, 2, 1, 12, 1, 2, 2, 2, 1, 12, 1, 2, 2, 2, 1, 12, 1, 2, 2, 2, 1, 12, 1, 2, 2, 2, 1, 12, 1, 2, 2, 2, 1, 12, 1, 2, 2, 2, 1, 12, 1, 2, 2, 2, 1, 12, 1, 2, 2, 2, 1, 12, 1, 2, 2, 2, 1, 12, 1, 2

Offset: 0

N. J. A. Sloane

			6.708203932499369089227521006... = 6 + 1/(1 + 1/(2 + 1/(2 + 1/(2 + ...)))). - _Harry J. Smith_, Jun 06 2009

James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 276.

Harry J. Smith, Table of n, a(n) for n = 0..20000
G. Xiao, Contfrac
Index entries for continued fractions for constants
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1).

Cf. A010499 (decimal expansion), A041076/A041077 (convergents).

ContinuedFraction[Sqrt[45],300] (* Vladimir Joseph Stephan Orlovsky, Mar 07 2011 *)

{ allocatemem(932245000); default(realprecision, 17000); x=contfrac(sqrt(45)); for (n=0, 20000, write("b010135.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 06 2009

G.f.: (6 + x + 2*x^2 + 2*x^3 + 2*x^4 + x^5 + 6*x^6)/(1 - x^6). - Stefano Spezia, Jul 27 2025

A041077 Denominators of continued fraction convergents to sqrt(45).

Original entry on oeis.org

1, 1, 3, 7, 17, 24, 305, 329, 963, 2255, 5473, 7728, 98209, 105937, 310083, 726103, 1762289, 2488392, 31622993, 34111385, 99845763, 233802911, 567451585, 801254496, 10182505537, 10983760033, 32150025603, 75283811239, 182717648081, 258001459320, 3278735159921

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,322,0,0,0,0,0,-1).

Cf. A010499, A041076.

Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[45],n]]],{n,1,50}] (* Vladimir Joseph Stephan Orlovsky, Mar 22 2011*)
Denominator[Convergents[Sqrt[45], 30]] (* Vincenzo Librandi, Oct 24 2013 *)
LinearRecurrence[{0,0,0,0,0,322,0,0,0,0,0,-1},{1,1,3,7,17,24,305,329,963,2255,5473,7728},40] (* Harvey P. Dale, Jun 11 2022 *)

a(n) = 322*a(n-6)-a(n-12). G.f.: -(x^10-x^9+3*x^8-7*x^7+17*x^6-24*x^5-17*x^4-7*x^3-3*x^2-x-1)/((x^2-3*x+1)*(x^2+3*x+1)*(x^4-3*x^3+8*x^2-3*x+1)*(x^4+3*x^3+8*x^2+3*x+1)). [Colin Barker, Jul 18 2012]

More terms from Vincenzo Librandi, Oct 24 2013

cp's OEIS Frontend

A010135 Continued fraction for sqrt(45).

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